Question

Find the quadratic equation whose solution set is `{-3, 2/5}`.

Answer 1

Since, `{-3, 2/5}` is solution set.

It means –3 and `2/5` are roots of the equation,

∴ x = –3 or x = `2/5`

⇒ x = –3 or 5x = 2

⇒ x + 3 = 0 or 5x – 2 = 0

⇒ (x + 3)(5x – 2) = 0

⇒ (5x² – 2x + 15x – 6) = 0

⇒ 5x² + 13x – 6 = 0

Hence, quadratic equation with solution set `{-3, 2/5}` is 5x² + 13x – 6 = 0.