SOLUTION: 1. Which of the following is a quadratic equation that has roots of 2 1/2 and 2/3? A) 5x^2 + 11x - 7 = 0 B) 6x^2 - 19x + 10 = 0 C) 5x^2 + 11x - 10 = 0 D) 6x^2 + 19x - 10 =

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: 1. Which of the following is a quadratic equation that has roots of 2 1/2 and 2/3? A) 5x^2 + 11x - 7 = 0 B) 6x^2 - 19x + 10 = 0 C) 5x^2 + 11x - 10 = 0 D) 6x^2 + 19x - 10 =       Log On


   

Question 611159: 1. Which of the following is a quadratic equation that has roots of 2 1/2 and 2/3?
A) 5x^2 + 11x - 7 = 0
B) 6x^2 - 19x + 10 = 0
C) 5x^2 + 11x - 10 = 0
D) 6x^2 + 19x - 10 = 0

14. Solve by completing the square x2 - 6x - 4 = 0.
21. Solve by completing the square x2 - 2x - 5 = 0.

25. Solve by completing the square 3x2 - 8x - 6 = 0.

26. Solve the quadratic equation x2 + 8x + 12 = 0.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. Which of the following is a quadratic equation that has roots of 2 1/2 and 2/3?
A) 5x^2 + 11x - 7 = 0
B) 6x^2 - 19x + 10 = 0
C) 5x^2 + 11x - 10 = 0
D) 6x^2 + 19x - 10 = 0
-------------------
(x - 5/2)*(x - 2/3) = 0
(2x - 5)*(3x - 2) = 0
6x%5E2+-+19x+%2B+10+=+0
--------------------------------
14. Solve by completing the square x2 - 6x - 4 = 0.
x%5E2+-+6x+=+4
x%5E2+-+6x+%2B+9+=+4+%2B+9
%28x-3%29%5E2+=+13
x+=+3+%2B+sqrt%2813%29
x+=+3+-+sqrt%2813%29
--------------------------
21. Solve by completing the square x2 - 2x - 5 = 0.
Same as #14
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25. Solve by completing the square 3x2 - 8x - 6 = 0
Divide by 3, then same as #14
-----------------------
26. Solve the quadratic equation x2 + 8x + 12 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%288%29%5E2-4%2A1%2A12=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+-2
x%5B2%5D+=+%28-%288%29-sqrt%28+16+%29%29%2F2%5C1+=+-6

Quadratic expression 1x%5E2%2B8x%2B12 can be factored:
1x%5E2%2B8x%2B12+=+%28x--2%29%2A%28x--6%29
Again, the answer is: -2, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B12+%29