Question

Write a quadratic equation whose zeroes are 5 and -5

Answer 1

let

$\alpha = 5$

$\beta = - 5$

then,

sum of the zeroes,

$\alpha + \beta = 5 + ( - 5) = 0$

product of the zeroes,

$\alpha \beta = ( - 5)(5) = - 25$

Now,

Quadratic equation =

$k \:( {x}^{2} - { 0x + ( - 25) }$

$k \: ( {x}^{2} - 25)$

therefore, the required equation is

${x}^{2} - 25$