Question

find a quadratic polynomial if the zeroes of it zeroes of it are 2 and _1/3 respectively​

Answer 1

Here's the Solution :

Given , the zeros are :

$\alpha = 2 \: and \: \: \beta = - \frac{1}{3} \\ \\ sum \: of \: the \: roots \\ \implies \alpha + \beta = 2 + \frac{ - 1}{3} \\ \implies \alpha + \beta = \frac{6 - 1}{3} \\ \implies \alpha + \beta = \frac{ - 5}{3} \\ \\ product \: of \: roots \\ \implies \alpha \beta = 2 \times ( - \frac{ 1}{3} ) \\ \implies \alpha \beta = \frac{ - 2}{3} \\ \\ now \: required quadratic\: \\ polynomial \: \\ \implies {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \implies \:{x}^{2} - \frac{ - 5}{3}x - \frac{2}{3} = 0 \\ \implies 3{x}^{2} + 5x - 2 = 0$

Solved