Question

if (x+a) is a factor of the polynomial x^2+px+q and x^2+mx+n thenprove that a = n-q/m-p

Answer 1

Answer:

If (x+a) is a factor of the polynomial x^2+px+q and x^2+mx+n then  $a=\frac{n-q}{m-p}$.

Step-by-step explanation:

The given polynomial are

$x^2+px+q$

$x^2+mx+n$

It is given that (x+a) is a factor of the polynomial. It means the value of polynomial is equal to 0 at x=-a.

$(-a)^2+p(-a)+q=0$

$(a)^2-ap+q=0$                       ..... (1)

$(-a)^2+m(-a)+n=0$

$(a)^2-am+n=0$               .... (2)

Equating (1) and (2), we get

$(a)^2-ap+q=(a)^2-am+n$

$(a)^2-ap+q-(a)^2+am-n=0$

$a(m-p)+q-n=0$

$a(m-p)=n-q$

$a=\frac{n-q}{m-p}$

Hence proved.

Answer 2

Answer:

Hope this helps you ✌️✌️