Question

Write a quadratic equation with roots –3 and 5.

Answer 1

Given: Roots are –3 and 5.

For roots α and β the quadratic is (x – α)(x – β) = 0.

Put α = –3 and β = 5:

(x – (–3))(x – 5) = (x + 3)(x – 5)

Expand: (x + 3)(x – 5) = x² – 5x + 3x – 15

= x² – 2x − 15

The quadratic equation with roots −3 and 5 is x² – 2x – 15 = 0.