Question

The polynomial whose zeroes are $\frac{5+\sqrt{3}}{3},\frac{5-\sqrt{3}}{3}$ is .

• A. 9x2-30x+22
• B. 9x2+30x+22
• C. x2+30x+22

Answer 1

The correct option is A 9x2-30x+22

Sum of zeroes = $\frac{5+\sqrt{3}}{3}+\frac{5-\sqrt{3}}{3}$= $\frac{10}{3}$
Product of zeroes = $\frac{5+\sqrt{3}}{3}\times \frac{5-\sqrt{3}}{3}$
$=\frac{5^2-(\sqrt{3}{)}^2}{9}=\frac{25-3}{9}=\frac{22}{9}$
Required polynomial $f\left(x\right)=\left[\right(x^2-\left(sumofzeroes\right)x+\left(productofzeroes\right)]$
$\Rightarrow \left[\right(x^2-\frac{10}{3}x+\frac{22}{9}$] [Multiplying by 9]
$\Rightarrow f\left(x\right)=9x^2-30x+22$