Story problem Algebra 1

Question

write an equation of the form (x^2) +bx +c =0 that has the solutions x=-3 and x=8. Explain how you found your answer 

Answer 1

Since -3 is a root, 9 - 3b + c = 0.  So, 3b - c = 9

Since 8 is a root, 64 + 8b + c = 0.  So, 8b + c = -64

 

Add the equations to get 11b = -55.  So, b = -5.

 

Since b = -5 and 3b - c = 9, -15 - c = 9.  So, c = -24.

Answer 2

If  x=c  is a root, then (x - c) is a factor of the function.

 

(x + 3)(x - 8) = 0

 

 

Now just expand.