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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