Question

Write the quadratic polynomial with zeros $-2$ and $\frac{1}{3}$.

Answer 1

The quadratic polynomial with zeros $\alpha ,\beta$ is,

$P\left(x\right)=k[x^2-(\alpha +\beta )x+\alpha \beta ]$

where, k is any non-zero real number.

$\therefore$ The quadratic polynomial with zeros $-2,\frac{1}{3}$ is,

$P\left(x\right)=k[x^2-(-2+\frac{1}{3})x+(-2\left)\right(\frac{1}{3}\left)\right]$

$=k[x^2+\frac{5}{3}x-\frac{2}{3}]$

where, k is any non-zero real number.