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

$x^{2}+7 x+12$

Solution:

$x^{2}+7 x+12=0$

$\Rightarrow x^{2}+4 x+3 x+12=0$

$\Rightarrow x(x+4)+3(x+4)=0$

$\Rightarrow(x+4)(x+3)=0$

$\Rightarrow(x+4)=0$ or $(x+3)=0$

$\Rightarrow x=-4$ or $x=-3$

Sum of zeroes $=-4+(-3)=\frac{-7}{1}=\frac{-(\text { coefficient of } x)}{\text { (coefficient of } x^{2} \text { ) }}$

Product of zeroes $=(-4)(-3)=\frac{12}{1}=\frac{\text { constant term }}{\text { coefficient of } x^{2}}$