Question

find the quadratic polynomial such that sum of its zeroes is 21 and difference between zeroes is 5

Answer 1

Hey!

$\alpha + \beta = 21$

$\alpha - \beta = 5$


Using identity :-

( a - b )² = ( a + b )² - 4ab

$( {5)}^{2} = {(21)}^{2} - 4 \alpha \beta$


$25 = 441 - 4 \alpha \beta$


$25 - 441 = - 4 \alpha \beta$



$- 416 = - 4 \alpha \beta$


$104 = \alpha \beta$


• To form quadratic equation :+

x² - Sum of Zeros x + product of Zeros = 0

x² - 21x + 104 = 0