SOLUTION: Suppose x1 and x2 are two solutions of the equation x^2+bx+c=0.Find x_1+x_2 and x_1 x_2. Hint: What are the solutions?

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Question 655375: Suppose x1 and x2 are two solutions of the equation x^2+bx+c=0.Find x_1+x_2 and x_1 x_2.
Hint: What are the solutions?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x1 and x2 are two solutions of the equation x%5E2%2Bbx%2Bc=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+...since a=1, we have

x+=+%28-b+%2B-+sqrt%28+b%5E2-4c+%29%29%2F2+

so, the solutions are:

x_1+=+%28-b+%2Bsqrt%28+b%5E2-4c+%29%29%2F2+

x_2+=+%28-b+-+sqrt%28+b%5E2-4c+%29%29%2F2+



now find x_1%2Bx_2 and x_1+%2A_2

x_1%2Bx_2=%28-b+%2Bsqrt%28+b%5E2-4c+%29%29%2F2%2B%28-b+-+sqrt%28+b%5E2-4c+%29%29%2F2

x_1%2Bx_2=%28-b+%2Bsqrt%28+b%5E2-4c+%29-b%2Bsqrt%28+b%5E2-4c+%29%29%2F2

x_1%2Bx_2=%28-2b+%2B2sqrt%28+b%5E2-4c+%29%29%2F2

x_1%2Bx_2=2%28-b+%2Bsqrt%28+b%5E2-4c+%29%29%2F2

x_1%2Bx_2=cross%282%29%28-b+%2Bsqrt%28+b%5E2-4c+%29%29%2Fcross%282%29

x_1%2Bx_2=-b+%2Bsqrt%28+b%5E2-4c+%29


and



x_1+%2A_2=%28-b+%2Bsqrt%28+b%5E2-4c+%29%29%2A%28-b+-+sqrt%28+b%5E2-4c+%29%29%2F%282%2A2%29





x_1+%2A_2=%28b%5E2+%2B+b%5E2-4c+%29%2F4

x_1+%2A_2=%282b%5E2-4c+%29%2F4

x_1+%2A_2=2%28b%5E2-2c+%29%2F4

x_1+%2A_2=cross%282%29%28b%5E2-2c+%29%2Fcross%284%29

x_1+%2A_2=%28b%5E2-2c+%29%2F2