Question

Find quadratic polynomial whose sum of zeros is 21/8 andproduct is 5/16

Answer 1

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Given ,

$\star$Sum of root = 21/8

$\star$Product of root = 5/16

We know that , formula of quadratic equation is :

$\large\fbox{ \fbox{ \sf \: {x}^{2} -(Sum \: of \: root)x + (Product \: of \: root) = 0 \: \: }}$

$\sf \to {x}^{2} - \frac{21}{8}x + \frac{5}{16} = 0 \\ \\ \sf \: \: \: \: Taking \: LCM \: , \: we \: get </p><p> \\ \\ \to \sf \frac{16 {x}^{2} - 42x + 5}{16} = 0 \\ \\ \sf \: \: \: \: By \: cross \: multiplication </p><p> \\ \\ \to \sf 16 {x}^{2} - 42x + 5 = 0$

$\therefore$16x² - 42x + 5 is the required quadratic polynomial