Question

If x = 3 is one root of the quadratic equation 2x² + px + 30 = 0, find the value of p and the other root of the quadratic equation.

Answer 1

Given, x = 3 is the root of quadratic equation

2x² + px + 30 = 0

∴ 2(3)² + p(3) + 30 = 0

⇒ 18 + 3p + 30 = 0

⇒ 3p = – 48

⇒ p = – 16

Now, the quadratic equation is 2x² – 16x + 30 = 0

⇒ x² – 8x + 15 = 0

⇒ x² – 3x – 5x + 15 = 0

⇒ x(x – 3) – 5(x – 3) = 0

⇒ (x – 3) (x – 5) = 0

⇒ x – 3 = or x – 5 = 0

⇒ x = 3 or x = 5

Hence, the other root of quadratic equation is 5.