SOLUTION: write a quadratic equation that has the solutions of -2 and 5

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Question 431049: write a quadratic equation that has the solutions of -2 and 5
Found 3 solutions by htmentor, ewatrrr, richard1234:
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The two solutions are x = -2 and x = 5
So the quadratic equation can be factored in the following way:
%28x+%2B+2%29%28x+-+5%29+=+0
Multiplying gives
x%5E2+-+3x+-+10+=+0
Check:
From the quadratic formula, the solutions are:
x+=+%283+%2B-+sqrt%283%5E2+%2B+4%2A10%29%29%2F2
This gives x = -2, 5

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

 y = (x+2)(x-5)

 y = x^2 -3x - 10

The factor theorem states that a polynomial f(x) has a factor (x- k) 

if and only if f(k) = 0

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
If -2 and 5 are roots, then x-(-2) and x-5 are factors of the polynomial. We can write the equation in the form

C(x+2)(x-5) = 0, where C is some nonzero constant.