Question

Write a quadratic polynomial whose zeroes are $2$ and $-6$.

Answer 1

$\Rightarrow$ Given zeros are $\alpha =2$ and $\beta =-6$.

$\Rightarrow$ Sum of zeros $=\alpha +\beta =2+(-6)=-4$

$\Rightarrow$ Product of zeros $=\alpha \times \beta =2\times (-6)=-12$

$\Rightarrow$ Quadratic polynomial $=x^2-(\alpha +\beta )x+(\alpha \times \beta )$

$\Rightarrow$ Quadratic polynomial $=x^2-(-4)x+(-12)$

$\therefore$ Quadratic polynomial $=x^2+4x-12$