Write an quadratic equation whose roots are 3 and -1/2. Explain your thinking?

Question

If you know then give it a try.

Answer 1

If the roots are a and b, the following factored quadratic equation is the result.

(x-a)(x-b) = 0

Your problem:

a = 3
b = -1/2

Therefore

(x-3)(x+1/2) = 0

Expand

x^2 -3x+1/2x -3/2 = 0

Multiply through by 2 and combine like terms.

2x^2 - 5x - 3 = 0