Question

if alpha+beta=5and alpha square+beta square=13 then find the quadratic equation whose roots are alpha and beta

Answer 1

our required equation is
(x-a)(x-b) = 0.... i am using a as alpha and b as beta
now a + b= 5
and (a^2) - (b^2) = 13
${a }^{2} - {b}^{2} = (a + b)(a -b )$
(a+b)(a-b) = 13
as a+b = 5
a - b = 13/5
add them both
2a = 38/5
a = 19/5
so b= 6/5
so equation is
( x-a )( x-b ) = 0
( x-19/5 )( x-6/5 ) = 0
(x^2) - 5x + 114/25 = 0
25(x^2) - 125x + 114 =0 ........multiplied by 25