SOLUTION: 12x2 + 23x + 10 = 0 A. 5/4, 2/3 B. -5/12, -1/5 C. -5/4, -2/3 D. 5/4, -2/3

Algebra ->  Algebra  -> Equations -> SOLUTION: 12x2 + 23x + 10 = 0 A. 5/4, 2/3 B. -5/12, -1/5 C. -5/4, -2/3 D. 5/4, -2/3      Log On

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Question 318139: 12x2 + 23x + 10 = 0
A. 5/4, 2/3 B. -5/12, -1/5 C. -5/4, -2/3 D. 5/4, -2/3
Answer by JBarnum(2044) About Me  (Show Source):
You can put this solution on YOUR website!
12x%5E2+%2B+23x+%2B+10+=+0 use quadratic formula
(-0.666666666666667, -1.25)
or (-2%2F3, -5%2F4)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B23x%2B10+=+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=%2823%29%5E2-4%2A12%2A10=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-23%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2823%29%2Bsqrt%28+49+%29%29%2F2%5C12+=+-0.666666666666667
x%5B2%5D+=+%28-%2823%29-sqrt%28+49+%29%29%2F2%5C12+=+-1.25

Quadratic expression 12x%5E2%2B23x%2B10 can be factored:
12x%5E2%2B23x%2B10+=+12%28x--0.666666666666667%29%2A%28x--1.25%29
Again, the answer is: -0.666666666666667, -1.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B23%2Ax%2B10+%29