Question

Find the quadratic equation whose solution set is `{2/5, -1/2}`.

Answer 1

Since, `{2/5, -1/2}` is solution set.

It means `2/5` and `-1/2` are roots of the equation,

∴ `x = 2/5` or `x = -1/2`

⇒ 5x = 2 or 2x = –1

⇒ 5x – 2 = 0 or 2x + 1 = 0

⇒ (5x – 2)(2x + 1) = 0

⇒ (10x² + 5x – 4x – 2) = 0

⇒ 10x² + x – 2 = 0

Hence, quadratic equation with solution set `{2/5, -1/2}` is 10x² + x – 2 = 0.