Question

Find the zeroes of the polynomial $x^2+x-p\left(p+1\right)$.

Answer 1

Step 1: Form the equation

The given polynomial is $x^2+x-p\left(p+1\right)$.

We know that the zeroes of a polynomial are evaluated by equating it with zero.

$\therefore p\left(x\right)=0$

$\Rightarrow x^2+x-p\left(p+1\right)=0$

Step 2: Solve to find the zeroes

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

$\Rightarrow x^2+\left(p+1\right)x-px-p\left(p+1\right)=0$

$\Rightarrow$ $x\left(x+p+1\right)-p\left(x+p+1\right)=0$

$\Rightarrow$ $\left(x+p+1\right)\left(x-p\right)=0$

$\Rightarrow$ $x=-\left(p+1\right),p$

Hence, the zeroes of this polynomial are $-\left(p+1\right)$ and $p$.