SOLUTION: I couldn't work letter C and #2, please assist. Please check the rest of the work and let me know if it is correct. Solutions of Quadratic Equations and their Applications

Question 193381: I couldn't work letter C and #2, please assist.
Please check the rest of the work and let me know if it is correct.
Solutions of Quadratic Equations and their Applications

1. Determine whether the following equations have a real or complex solution. Justify your answer.
a) x2 + 3x - 15 = 0
a = 1
b = 3
c = -15
Discriminant: b2-4ac = 3 2-4*1*(-15) = 69
Discriminant (69) is greater than zero. The equation has two solutions
b) x2 + x + 4 = 0
a = 1
b = 1
c = 4
Discriminant: b2-4ac = 1 2-4*1*4 = -15
Discriminant (-15) is less than zero. No solutions are defined.
c)

d) x2 � 8x + 16 = 0
a = 1
b = -8
c = 16
Discriminant: b2-4ac = 8 2-4*1*16 = 0
Discriminant (0) is zero. There is only one solution.
e) 2x2 - 3x + 7 = 0
b = -3
c = 7
Discriminant: b2-4ac = 3 2-4*2*7 = -47
Discriminant (-47) is less than zero. No solutions are defined.

f) x2 � 4x - 77 = 0
a = 1
b = -4
c = -77
Discriminant: b2-4ac = 4 2+4*1*(-77) = 324
Discriminant (324) is greater than zero. The equation has two solutions
g) 3x2 - 7x + 6 = 0
a = 3
b = -7
c = 6
Discriminant: b2-4ac = 7 2-4*3*6 = -23
Discriminant (-23) is less than zero. No solutions are defined.
h) 4x2 + 16x + 16 = 0
a = 4x
b = 16
c = 16
Discriminant: b2-4ac = 16 2-4*4*16 = 0
Discriminant (0) is zero. There is only one solution.

2. Find an equation for which -3 and 4 are solutions.

3. What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solution of the equation.
You get complex solutions for b^2-4ac<0.
x^2 +4x +5 = 0
x = [-4 +/-(16-20)^1/2]/2 = -2 +/-i

4. Create a real-life situation that fits the equation (x + 3)(x - 5) = 0 and express the situation as the same equation.
The length of a rectangular field is 2 feet more than the width and the area of the field is 15 sq feet.
Here is how we arrived at the equation from real life situation -
Let the length be x, then width = x-2,
and area = length * width
so. x(x-2) = 15
so, x^2 - 2x -15 =0
Factoring we get
(x+3)(x - 5) = 0
so, x=5 (as lenth has to be positive)
hence width = 3 feet
Found 2 solutions by yuendatlo, solver91311:
Answer by yuendatlo(23) (Show Source): You can put this solution on YOUR website!
eefg
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

1a. Correct.

1b. You calculated the discriminant correctly, but interpreted the results incorrectly. You said that there are no defined solutions. In fact, there are no real number solutions. However, there is a conjugate pair of complex solutions -- see your answer to #3. Even if your instructor wanted you to answer "No solution" to these, you should still say "No real number solution"

1c. Can't help you with this one. You didn't include the problem.

1d. Almost correct. You should say that there is one real number solution with a multiplicity of 2.

1e. Same answer as 1b.

1f. Correct.

1g. Same answer as 1b.

1h. Same answer as 1d.

2. If -3 and 4 are solutions, then and are the factors of the quadratic trinomial, so:

3. Correct

4. Correct

John

RELATED QUESTIONS
Hello. A square has sides of length 3x-2 cm. Express the area of the square as a... (answered by stanbon)
You are stationed at a port on the ocean. A cruise liner is sailing past your port. When... (answered by math_tutor2020)
Sorry, tried to put the shape in, couldn�t work, only let print the words. The star... (answered by solver91311)
Hats may be ordered from a supplier for $7.50 each or $60 for ten. Mrs Smith orders some (answered by Edwin McCravy,MathTherapy)
Okay, so I'm really struggling on this question, and I was wondering if someone could... (answered by MathLover1,ikleyn)
Please help me solve this question. A curve has the equation {{{y=acosbx+c}}} , with (answered by Theo)
Hello, my question is a pre-algebra one and I have tried to work it out like this, but... (answered by xcentaur)
14. 15t^2-17t-4 (5t-3)(t-4) Tried to work it out don't know if this is the right... (answered by oberobic)
I am having trouble with a question, and I think I know the answer and I just need... (answered by Pieter)