Question

Find a quadratic polynomial, the sum and product of whose zeroes are $\frac{5}{6}$ and $\frac{1}{3}$ respectively.

Answer 1

Find the quadratic polynomial:

We know that the quadratic polynomial whose zeroes are $\mathrm{a}$ and $\mathrm{b}$ is $x^2-(a+b)x+ab$

Sum of the zeroes $=\frac{5}{6}$

$=a+b$

Product of the zeroes $=\frac{1}{3}$

$=ab$

Then the quadratic polynomial is:

$$\begin{gathered} p\left(x\right)=x^2-\left(\frac{5}{6}\right)x+\left(\frac{1}{3}\right) \\ =6x^2-5x+2 \end{gathered}$$

Hence, the required quadratic polynomial is $6x^2-5x+2$