Question

If x + a is a factor of ma - nx - 3x2 then prove that a = m + n / 3

Answer 1

I hd done it
Hope u understand it
Good luck buddy....!!!

Answer 2

$a=\dfrac{m+n}{3}$, proved.

Step-by-step explanation:

Let the given polynomial P(x) : $ma-nx-3x^2$   ....... (1)

Given, (x + a) is a factor of P(x).

To prove that, $a=\dfrac{m+n}{3}$.

∴ x + a = 0

⇒ x = - a

Put x = - a in equation (1), we get

$P(x)=ma-n(-a)-3(-a)^2=0$

⇒ $ma+na-3a^2=0$

⇒ $-3a^2+ma+na=0$

⇒ $-3a^2+(m+n)a=0$

⇒ $3a=m+n$

⇒ $a=\dfrac{m+n}{3}$

∴ $a=\dfrac{m+n}{3}$

Hence, $a=\dfrac{m+n}{3}$, proved.