Question

find the zeros of the polynomial mx2+(m+n)x+n

Answer 1

Answer to your question:

Given,

The polynomial,
mx²+(m+n)x+n

=mx²+(m+n)x+n
=mx²+mx+nx+n
=mx(x+1)+n(x+1)
=(x+1)(mx+n)

We get (x+1)=0, (mx+n)=0
So, according to the rule, the value of x will be the zeros of the polynomial.
Either, x+1=0 => x=-1 or mx+n=0 => mx=-n => x =-n/m
Hence, the zeros of the polynomial are -1,-n/m

Answer 2

mx² + (m + n)x + n
= mx² + mx + nx + n
= mx(x + 1) + n(x + 1)
= (mx + n)(x + 1)

Here you can see (mx + n) and (x + 1) are the factors of given polynomial mx² + (m + n)x + n , so (mx + n) = 0 ⇒x = -n/m and (x + 1) = 0 ⇒x = -1 are the zeros of given polynomial .

Hence, zeros of polynomial are -n/m and -1