SOLUTION: How would you find the sum and product of the root of this quadratic equation? 1.{{{ 2x^2+8x-3=0 }}}

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Question 6334: How would you find the sum and product of the root of this quadratic equation?
1.+2x%5E2%2B8x-3=0+
Found 2 solutions by ichudov, Yuchengco:
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
one easy way to do it is to just bite the bullet and solve the equation and then find out sum and product of roots x1 and x2. Another is to note that for equations x%5E2+%2B+bx+%2B+c+=0, b is the sum of roots and c is their product.
that means looking at equation x^2+4x-3/2 = 0. sum is 4, product is -3/2.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B8x%2B-3+=+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%2A2%2A-3=88.

Discriminant d=88 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+88+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+88+%29%29%2F2%5C2+=+0.345207879911715
x%5B2%5D+=+%28-%288%29-sqrt%28+88+%29%29%2F2%5C2+=+-4.34520787991172

Quadratic expression 2x%5E2%2B8x%2B-3 can be factored:
2x%5E2%2B8x%2B-3+=+2%28x-0.345207879911715%29%2A%28x--4.34520787991172%29
Again, the answer is: 0.345207879911715, -4.34520787991172. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B8%2Ax%2B-3+%29

Answer by Yuchengco(1) About Me  (Show Source):
You can put this solution on YOUR website!
r1+r2=-B/A
r1*r2=C/A
AX^2+BX+C=0 is the standard form
2X^2+8X-3=0
sum of roots = -8/2 = -4
Product of roots= -3/2