Questions on Algebra: Quadratic Equation answered by real tutors!

Tutors Answer Your Questions about Quadratic Equations (FREE)

Question 1207376: Wendy wants to build a frame of uniform width around the outside of her 21cm x 30cm photo but she can only afford 188cm² of wood for the frame. How wide will the frame be?
Click here to see answer by mccravyedwin(405)

Question 1207404: Find the real solutions, if any, of the given equation.

(3/4)x^2 - (1/4)x - (1/2) = 0

Let me see.

I can use the quadratic formula. In the formula, a = 3/4, b = -1/4 and c = -1/2.

Yes?
Click here to see answer by math_tutor2020(3816)

Question 1207405: Find the real solutions, if any, of the two given equations.

x^2 + 3.9x + 1.8 = 0

Using the quadratic formula, a = 1, b = 3.9 and c = 1.8.

Yes?

How about this one?

pi•x^2 + pi•x - 2 = 0

Again, Using the quadratic formula, a = pi, b = pi and c = -2.

You say?
Click here to see answer by ikleyn(52759)

Question 1207406: Use the discriminant to determine whether each quadratic equation has two unequal real solutions,a repeated real solution,or no real solution,without solving the equation.

x^2 + 4x + 7 = 0

I know the discriminant is the radicand of the quadratic formula.

So, I need to use b^2 - 4ac where a = 1, b = 4 and c = 7.

b^2 - 4ac

(4)^2 - 4(1)(7)

16 - 28 = -12

The answer is -12.

The discriminant is negative, which means the equation has no real solution.

You say?

What would be an example of a repeated real solution or no solution at all?

Click here to see answer by ikleyn(52759)

Question 1207450: Show that the product of the roots of a quadratic equation is c/a.
I see the word product in the application. This tells me to multiply two quadratic formulas and simplify to get c/a.
Yes?
Click here to see answer by Theo(13342)

Question 1207449: Show that the sum of the roots of a quadratic equation is -b/a.

I know this involves the quadratic formula but not sure of the set up.
Do I add or multiply two quadratic formulas to get -b/a?
Click here to see answer by ikleyn(52759)

Question 1207457: Find k such that the equation x^2 - kx + 4 = 0 has a repeated real solution.

Let me see.

I think the discriminant applies here.

b^2 - 4ac = 0

k^2 - 4(1)(4) = 0

k^2 - 4(4) = 0

k^2 - 16 = 0

k^2 = 16

sqrt{k^2} = sqrt{16}

k = -4 or k = 4

A. Is this correct?
B. If so, does k = -4 or does k = 4?
Click here to see answer by ikleyn(52759)

Question 1207458: Show that the real solutions of the equation ax^2 + bx + c = 0 are the reciprocals of the real solutions of the equation cx^2 + bx + a = 0. Assume that b^2-4ac is greater than or equal to 0.

Do I equate both equations? If not, how is this done?
Click here to see answer by math_tutor2020(3816)

Question 1207491: The cost function for a certain company is
C = 40x + 800
and the revenue is given by
R = 100x − 0.5x2.
Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $800.
Click here to see answer by MathLover1(20849)

Question 1207526: The following function models the average typing speed S, in words per minute, of a student who has been typing for t months.
S(t) = 4 + 31 ln(t + 1), 0 ≤ t ≤ 16
(a) What was the student's average typing speed, to the nearest word per minute, when the student first started to type?
What was the student's average typing speed, to the nearest word per minute, after 3 months?

(b) Use a graph of S to determine how long, to the nearest tenth of a month, it will take the student to achieve an average typing speed of 50 words per minute.

Click here to see answer by MathLover1(20849)

Question 1207537: Provided GT is a median.
Find TE if FT = 36

then, Provided GT is a median.
Find TE if FE =114

then, Provided FI is a median.
Find x if GE =5x+7 and IE = 2x+5

Click here to see answer by ikleyn(52759)

Question 1207562: If the roots of the equation ax^2 + bx + c is equals to zero are alpha and beta find the equation whose roots are Alpha square and beta square
Click here to see answer by mananth(16946)

Question 1207564: The area of a playground is 153 m square if the length of the playground is decreased by 4 m and the breadth is increased by 4 m if playground become a square decide of the square in metre is
Click here to see answer by mananth(16946)

Question 1207560: The sides of a right angled triangle are such that the sum of the length of the
longest and that of the shortest side is twice the length of remaining side, the
longest side of the triangle if the longer of the sides containing the right
angle is 9 CM more than half the hypotenuse is??
Click here to see answer by greenestamps(13196)

Question 1207563: If x + y is equals to 4 find maximum or minimum
possible value of x square + y square

Click here to see answer by josgarithmetic(39614)

Question 1207563: If x + y is equals to 4 find maximum or minimum
possible value of x square + y square

Click here to see answer by Edwin McCravy(20054)

Question 1207561: the roots of the equation ax^2 + bx + c is equals to zero are k less than those of the equation px² + qx + r is equals to zero. Find the equation whose roots are a more than those of px² + qx +r=0
Please help me solve this question
Click here to see answer by mccravyedwin(405)

Question 1207661: Find the real solutions of the equation.

2x^(-2) - 3x^(-1) - 4 = 0

I then decided to rewrite the original equation this way:

(2/x^2) - (3/x) - 4 = 0

Stuck here....
Click here to see answer by Theo(13342)

Question 1207838: Given (1/x) = (1/a) + (1/b),
1. Solve to show x = ab/(a + b), provided that a + b does no equal 0.
2. Check the solution.
Click here to see answer by josgarithmetic(39614)

Question 1207920: A garden 7 m by 12 m will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an area of 92 im
Click here to see answer by ikleyn(52759)

Question 1208084: Let y = piecewise function.

Top portion of y = 1 if x is rational.

Bottom portion of y = 0 if x is irrational.

Is this a function? What is its domain? What is its range? What is its y-intercept, if any? What are its x-intercepts, if any? Is it even,odd,or neither? How would you describe its graph?
Click here to see answer by math_tutor2020(3816)

Question 1208115: Complete the square for each quadratic equation.

A. f(x) = 3x^2 + 6x + 2

B. g(x) = -2x^2 - 12x - 13
Click here to see answer by ikleyn(52759)

Question 1208115: Complete the square for each quadratic equation.

A. f(x) = 3x^2 + 6x + 2

B. g(x) = -2x^2 - 12x - 13
Click here to see answer by josgarithmetic(39614)

Question 1208115: Complete the square for each quadratic equation.

A. f(x) = 3x^2 + 6x + 2

B. g(x) = -2x^2 - 12x - 13
Click here to see answer by timofer(104)

Question 1208115: Complete the square for each quadratic equation.

A. f(x) = 3x^2 + 6x + 2

B. g(x) = -2x^2 - 12x - 13
Click here to see answer by math_tutor2020(3816)

Question 1208130: Let P = (x,y) be a point on the graph of y = 1/x.
A. Express the distance d from P to the origin as a function of x.
B. Use a graphing utility to graph d = d(x).
Click here to see answer by math_tutor2020(3816)

Question 1208129: Let P = (x,y) be a point on the graph of y = x^2 - 8.
(a)Express the distance d from P to the point as a function of x.
(b) What is d if x = 0?

Click here to see answer by math_tutor2020(3816)

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