Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
Question:

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

$x^{2}-2 x-8$

 

Solution:

$x^{2}-2 x-8=0$

$\Rightarrow x^{2}-4 x+2 x-8=0$

$\Rightarrow x(x-4)+2(x-4)=0$

$\Rightarrow(x-4)(x+2)=0$

$\Rightarrow(x-4)=0$ or $(x+2)=0$

$\Rightarrow x=4$ or $x=-2$

Sum of zeroes $=4+(-2)=2=\frac{2}{1}=\frac{-(\text { coefficient of } x)}{\text { coefficient of } x^{2}}$

Product of zeroes $=4(-2)=-8=\frac{-8}{1}=\frac{\text { constant term }}{\text { coefficient of } x^{2}}$

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