Question

Find a quadratic equation whose roots are root 2 and 1/3

Answer 1

Given the roots 2 and 1/3

$\alpha = 2 \\ \beta = \frac{1}{3} \\ \\ sum \: of \: the \: roots \: \\ \alpha + \beta = 2 + \frac{1}{3} \\ \\ = > \alpha + \beta = \frac{6 + 1}{3} \\ \\ = > \alpha + \beta = \frac{7}{3} \\ \\ product \\ \alpha \beta = 2 \times \frac{1}{3} \\ \\ = > \alpha \beta = \frac{2}{3} \\ \\ required \: equation \\ {x}^{2} - ( \alpha + \beta )</em><em>x</em><em> + \alpha \beta = 0 \\ \\ = > {x}^{2} - \frac{7}{3} x + \frac{2}{3} = 0 \\ \\ = > \frac{3 {x}^{2} - 7x + 2 }{3} = 0 \\ \\ = > 3 {x}^{2} - 7x + 2 = 0$