Write the zeros of the polynomial x2 − x − 6.

Question:

Write the zeros of the polynomial $x^{2}-x-6$

Solution:

We have to find the zeros of the polynomial $x^{2}-x-6$

$f(x)=x^{2}-x-6$

$f(x)=x^{2}-3 x+2 x-6$

$f(x)=x(x-3)+2(x-3)$

$f(x)=(x+2)(x-3)$

We know that if $(x-\alpha)$ is a factor of $f(x)$ then $x=\alpha$ is a zero of polynomial

Therefore we have

$x+2=0$

$x=-2$

Also

$x-3=0$

$x=3$

Hence, the zeros of polynomial $x^{2}-x-6$ is $3,-2$

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