Find the zeros of the polynomial $ x^{2}+x-p(p+1) $.



Given:

Given polynomial is $x^{2}+x-p(p+1)$.

To find:

We have to find the zeros of the given polynomial. 

Solution:

To find the zeros of g(x), we have to put $g(x)=0$.

This implies,

$x^2+x-p(p+1)=0$

$x^2+(p+1)x-px-p(p+1)=0$

$x[x+(p+1)]-p[x+(p+1)]=0$

$[x+(p+1)](x -p)=0$

$x+(p+1)=0$ or $x-p=0$

$x = -(p+1)$ or $x = p$

Therefore, the zeros of the polynomial \( x^{2}+x-p(p+1) \) are $-(p+1)$ and $p$.

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