Question

1. If (x - a) is one of the factors of the polynomial
ar + bx+c, then one of the roots of ax + bx+c=0 is

Answer 1

Step-by-step explanation:

(x-a) is a factor of the polynomial ax+bx+c

Therefore a is a zero of the polynomial.

a(a) +b(a) +c=0

a^2+ba+c=0

Dividing this equation with (x-a), we get the quotient as (x+a)

Therefore (x+a) is a also factor of the polynomial and (- a) is also a zero of the polynomial

Answer 2

(x + a) is a factor of the given polynomial and (- a) is also a zero of the polynomial.

Step-by-step explanation:

Given,

$x-a$ is a factor of the polynomial P(x) = $ax+bx+c$

To find, the one of the roots of $ax+bx+c=0$

∴$x-a=0$

⇒ x = a

Put x = a in the given  polynimial, we get

$P(a)=a(a)+b(a)+c=0$

$a^2+ab+c=0$

Dividing this equationby $(x-a)$, we get

Quotient = x + a

Hence,  (x + a) is a factor of the given polynomial and (- a) is also a zero of the polynomial.