Question

Find the zeros of the quadratic polynomial $x^2+9x+20$, and verify the basic relationships between the zeros and the coefficients.

Answer 1

Let $p\left(x\right)=x^2+9x+20=(x+4)(x+5)$

So, $p\left(x\right)=0\to (x+4)(x+5)=0$

$\therefore x=-4$ or $x=-5$

Thus, $p(-4)=(-4+4)(-4+5)=0$ and $p(-5)=(-5+4)(-5+5)=0$

Hence, the zeros of ( ) p x are -4 and -5 Thus, sum of zeros = -9 and the product of zeros 20 = (1)

From the basic relationships, we get

the sum of the zeros $=-\frac{coefficientofx}{cofficient{x}^2}=\frac{9}{1}=-9$ (2)

product of the zeros $=\frac{constantterm}{cofficient{x}^2}=\frac{20}{1}=20$ (3)

Thus, the basic relationships are verified.