Questions on Algebra: Quadratic Equation answered by real tutors!

Tutors Answer Your Questions about Quadratic Equations (FREE)

Question 31251: Hi! I need to find all real solutions of this equation:
x^6-2x^3-3=0
I don't think there are any real solutions as I can't factor it right (x^3+1)(x^3-3)=0.
Thank you all so much!
Click here to see answer by longjonsilver(2297)

Question 31275: I have a work sheet with quadratic equations and i don't understand it at all. It read's: Solve the equation by factoring, 3xsquared+9x-12=0.(how do i factor this where do i start?)my teacher showed me how but i can't remember can you please help me?
Click here to see answer by mukhopadhyay(490)

Question 31338: find two consecutive positive intergers such that the square of the smaller increased by four times the larger is 64.
Click here to see answer by Paul(988)

Question 31337: in a rectangular garden whose area is 24 Square centimeters, the length is 5 centimeters more than the width. find the dimensions of the garden.
Click here to see answer by Nate(3500)

Question 31335: in a rectangular garden whose area is 24 centimeters, the length is 5 centimeters more than the width. find the dimensions of the garden.
Click here to see answer by Nate(3500)

Question 31334: the square of a certain number minus nine times the number is 36. find the number.
Click here to see answer by stanbon(75887)

Question 31333: find two consecutive integers such that the sum of their squares is 61.
Click here to see answer by checkley71(8403)

Question 31323: Hi,
I'm trying to find all real solutions to this equation:
4x^-4-16x^-2+4=0
I have:
4/x^4-16/x^2+4=0
multiplying by x^4:
4-16x^2+4=0
4x^4-16x^2+4=0
4(x^4-4x^2+1) = 0 (unfactorable?)
a=1;b=4;c=1
Using the quadratic equation I get:
-4+-sq root of 3, but this doesn't seem right.
Thanks for all your help!
Click here to see answer by longjonsilver(2297)

Question 31365: The axis of symmetry of a parabola is the line x=2. The point (4,-4) lies on the parabola. Use the symmetry of a parabola to find a second point on the graph.
Could someone tell me if I am supposed to be using a formula to solve this? I can't figure it out and feel like I'm overlooking the obvious!
Click here to see answer by stanbon(75887)

Question 28934: Hi,
I'm currently studying solving quadratic inequalities, and I'm having a bit of trouble.
I'm trying to solve 1/2x^2 + 3x (less than or equal to) -6. Since I couldn't factor the equation, I tried using the quadratic formula, however I got a complex number. I'm not exactly sure how to test the complex numbers, so I'm a bit lost on how to solving this.
Thanks for any help you can provide!
Click here to see answer by Fermat(136)

Question 31462: HI... I cannot figure this out...
Solve the equation by using athe quadratic formula. Give only real number solutions....
4n ^ 2 = -6n - 1
Click here to see answer by blubunny01(20)

Question 31457: A manufacturer of microwave ovens believes that the revenue R, in dollars, the company receives is related to the price P, in dollars, of an oven given by the function R(P)=125P-0.25P^2. What price of an oven will give the maximun revenue?
-(b/(2a)=
-(125)/(2*-.25)=
-(125/.5)=250
Price of an oven=$250.00
This answer matches my book but my question is doesn't 250= the x coordinate of the vertex and then shouldn't I be solving for the y coordinate to get the maximum revenue? Meaning why don't I then substitute 250 for x and solve for y or am I confusing the use of the phrase "maximum revenue" with a maximum value of a quadratic function problem?

Click here to see answer by stanbon(75887)

Question 31450: using the quadratic equation x2-4x-5=0 perform the following task:
solve by completing the square.
how do i do this im lost thank you.
Click here to see answer by Earlsdon(6294)

Question 31425: 1. 2x^2 - 7x + 5 =0
2. 3x^2 + 10x + 5 =0
3. -5 + or - the square root of 10 / 3

Click here to see answer by ikdeep(226)

Question 31494: Let p,q be the roots of the equation (x-a)(x-b)=c with c<>0.Then the roots of the equation (x-p)(x-q)+c=0 are which of the following:-
A.a,b
B.a,c
C.b,c
D.a,b,c
Click here to see answer by mukhopadhyay(490)

Question 31632: 3) Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
� 16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
� v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
� s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
1. How long will it take to hit the ground?
2. What is the maximum height of the ball? What time will the maximum height be attained?

Click here to see answer by Earlsdon(6294)

Question 31653: Fireworks Problem...
t: elapsed time in seconds
v0: initial upward velocity in feet per second
h(t): altitude in feet
Let , where v0 is positive.
A. Use the disciminant to show that there are always two elapsed times at which altitude is 0.
B. Use your answer to part A or an analysis of quadratic functions to find the maximum altitude of the rocket.
Thank you!
Click here to see answer by mbarugel(146)

Question 31077: 2 ferryboats leave opposite sides of a lake at the same time. They pass eachother when they are 800 meters from the nearest shore. When it reaches the opposite side, each boat spends 30 minutes at the dock and then starts back. This time the boats travels at the same speed in both directions, how wide is the lake between the two ferry docks? You must use a quadratic equation.
Thank you
Click here to see answer by venugopalramana(3286)

Question 31503: 5.If a+b+c=0,then 3a*x*x+2b*x+c=0 has
A.atleast one root in [-1,0]
B.atleast one root in [0,1]
C.atleast one root in [-1,1]
D.atleast one root in [0,2]
Click here to see answer by venugopalramana(3286)

Question 31789: Derive the quadratic formula by completing the square for:
ax squared + bx + c = 0
Click here to see answer by Earlsdon(6294)

Question 31840: WELL I KNOW HOW TO GET THE VERTEX OF A QUADRATICS EQUATION BUT I DONT GET HOW TO GET OR FIND THE ROOT FOR EXAMPLE FINDIN THE ROOT OF THIS PROBLEM:
Y=(x-2)(x+6)
Click here to see answer by stanbon(75887)

Question 31868: A square pool has length p. The border of the pool is 1 ft. wide. The combined area of the border and the pool is 400ft squared. Find the area of the pool
Click here to see answer by Paul(988)

Question 31837: If Y varies inversely as X^2 and Y=2 X=4.
What is the constant of variation?
Click here to see answer by venugopalramana(3286)

Question 31884: John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be?

I aslo get 50 x100 dont think that is correct? Please help
Click here to see answer by mbarugel(146)

Question 29985: For csc^2 a- 1/cotA cscA--what is the simplest equivalent trigonometric expression
Click here to see answer by venugopalramana(3286)

Question 31919: 1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks:
a) Solve by factoring.

b) Solve by completing the square.
c) Solve by using the quadratic formula.

Click here to see answer by mukhopadhyay(490)

Question 31972: Solve the following quadratic equations by using an optimum method.
x^2 - 9x - 4 = 6
Please help.
Thank you.
Click here to see answer by stanbon(75887)

Question 31920: When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.
Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.
Click here to see answer by elima(1433)

Question 31971: Solve the quadratic equations by using an optimum method.
(x - 1)^2 = 7
I really need help.
Thanks you.
Click here to see answer by stanbon(75887)

Question 31989: how do u solve this: x^2-4x+1=0
Click here to see answer by stanbon(75887)

Question 31999: Find all real or imaginary solutions.
Square Root symbol 7x + 29 = x + 3
Textbook Elementary and Intermediate Algebra. Mark Dugopolski
ISBN: 13978-0-07-326862-0

Click here to see answer by Earlsdon(6294)

Question 32006: Determine whether the graph of each parabola opens upward or downward.
y= -1/2^x^2+3
Please help me to understand what parabola means.

Textbook Elementary and Intermediate Algebra. Mark Dugopolski
ISBN: 13978-0-07-326862-0

Click here to see answer by Earlsdon(6294)

Question 32003: Story Problem
The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures square root symbol 6m. find the width and height.

Textbook Elementary and Intermediate Algebra. Mark Dugopolski
ISBN: 13978-0-07-326862-0

Click here to see answer by Paul(988)

Question 32016: 4x² = 35 - 4x
Thank you
Click here to see answer by AnlytcPhil(1806)

Question 32024: The frame of a picture is 28cm by 32cm outside and is of the uniform width. What is the width of the frame if 192cm^2 of the picture shows?
Click here to see answer by Paul(988)

Question 32040:

I'm totally stuck!  I've tried working it but I seem to get stuck on the same

spot!  Here's the problem: 



For the function y = x² - 4x - 5, perform the following tasks:



a) Put the function in the form y = a(x - h)² + k.



b) What is the line of symmetry?

	

c) Graph the function using the equation in part a.  Explain why it is not

necessary to plot points to graph when using y = a (x � h)² + k.



d) In your own words, describe how this graph compares to the graph of

   y = x²?



For "a", I got y=(x-2)² - 14.  From there, I'm totally lost!  Can somebody

help!  (P.S.  I haven't taken algebra since high school and that was 15 yrs

ago!)  :-)_



Thanks!

 


Click here to see answer by Earlsdon(6294)

Question 32040:

I'm totally stuck!  I've tried working it but I seem to get stuck on the same

spot!  Here's the problem: 



For the function y = x² - 4x - 5, perform the following tasks:



a) Put the function in the form y = a(x - h)² + k.



b) What is the line of symmetry?

	

c) Graph the function using the equation in part a.  Explain why it is not

necessary to plot points to graph when using y = a (x � h)² + k.



d) In your own words, describe how this graph compares to the graph of

   y = x²?



For "a", I got y=(x-2)² - 14.  From there, I'm totally lost!  Can somebody

help!  (P.S.  I haven't taken algebra since high school and that was 15 yrs

ago!)  :-)_



Thanks!

 


Click here to see answer by AnlytcPhil(1806)

Question 31988: how do u solve this: 3xsquared-2=4x
Click here to see answer by mukhopadhyay(490)

Question 32063: WHAT DOES THIS SYMBOL MEAN ^?
Click here to see answer by Earlsdon(6294)

Question 32049: I emailed you last night but was having computer problems, so thought I would try again. I am having problems decifering the difference between: solve by factoring, solve by completing the square, and solve by using the quadratic equation.
1) Using the quadratic equation x squared-4x-5=0, solve by factoring, solve by completing the square, and solve by using the quadratic formula.
Question 2) I don't know how different letters can replace other letters: For the function y=x squared-4x-5, put the function in the form y=a(x-h)squared+k. What is the line of symmetry? Graph the function using the equation in the first part. Explain why it is not necessary to plot points to graph when using y=a(x-h)squared+k.
Do you know where I can find the squared key and square root key?
Click here to see answer by stanbon(75887)

Question 31996: Find all real or imaginary solutions.
w^2=-225
Textbook Elementary and Intermediate Algebra. Mark Dugopolski
Page 628, Question 78
ISBN: 13978-0-07-326862-0

Click here to see answer by ikdeep(226)

Question 31990: how do u solve this problem 1-5xsquared=-3x
Click here to see answer by mukhopadhyay(490)

Question 32147: 3) Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
� 16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
� v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
� s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
a) What is the function that describes this problem?
b) The ball will be how high above the ground after 1 second?
c) How long will it take to hit the ground?
d) What is the maximum height of the ball? What time will the maximum height be attained?

Click here to see answer by stanbon(75887)

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