Question

Find the zeroes of the quadratic polynomial $x^2+x-2$, and verify the relationship between the zeroes and coefficients.

Answer 1

We have,

$x^2+x-2=0$

$(x+2)(x-1)=0$

$x=-2,1\dots \left(1\right)$

Relation between zeroes and quadratic polynomial can be verified by sum of roots and product of roots.

Let $\alpha$ and $\beta$ be two roots which are equal to$-2$ and $1$ respectively.$\dots from\left(1\right)$

As we know,

$\alpha +\beta =\frac{-b}{a}$

$\Rightarrow \frac{-1}{1}=-1$

$\alpha \beta =\frac{c}{a}$

$\Rightarrow \frac{-2}{1}=-2$

Hence, the relationship between zeros and coefficients of polynomial is verified.