Question

Find the value of "a" in the polynomial 2a + 2xa + 5a + 10 if (a + x) is one of its factors.

Answer 1

If a + x is a factor of polynomial P(x)

then x = -a is a root of P(x).

∴ P(-a) = 0

⇒ 2a + 2(-a)a + 5a + 10 = 0

⇒ -2a² + 7a + 10 = 0

⇒ \(a = \frac{-7 \pm \sqrt{49 + 80}}{-4}\)

\(= \frac{7\pm \sqrt{129}}{4}\)