Question

Find a quadratic polynomial if the zeroes of it are $2$ and $-\frac{1}{3}$ respectively.

Answer 1

Given: Zeros of a quadratic equation are $2$ and $-\frac{1}{3}$.

Sum of zeros $=-\frac{1}{3}+2=-\frac{5}{3}$

Product of zeros $=-\frac{1}{3}\times 2=-\frac{2}{3}$

The quadratic equation is given by the formula when we have sum of zeros and product of zeros

$x^2-\left(\text{sum of zeroes}\right)x+\text{product of zeroes}=0$

$\Rightarrow x^2-\left(\frac{-1}{3}+2\right)x+2\times (-\frac{1}{3})=0$

$\Rightarrow x^2-\frac{5x}{3}-\frac{2}{3}=0$

$\Rightarrow 3x^2-5x-2=0$ [on multiplying both sides by $3$]

Therefore, the required quadratic equation is $3x^2-5x-2=0$.