The roots alpha and beta of the quadratic equation x2-5x +3(k-1) = 0 are such that alpha - beta= 11 - Maths - Quadratic Equations

Question

The roots alpha and beta of the quadratic equation x2-5x +3(k-1)
= 0 are such that alpha - beta= 11 Find the value of k

S. Usha Rani · Accepted Answer

Given
α-β=11 (1)Since α and β are roots of
x2-5x+3(k-1)=0,sum of roots=-ba=-(-5)1=5So, α+β=5
(2)(1)+(2) gives,2α=16α=8Since α=8 is a root, it
will satisfy the given equation
So,82-5(8)+3(k-1)=064-40+3k-3=03k=-21k=-7

The roots alpha and beta of the quadratic equation x2-5x +3(k-1) = 0 are such that alpha - beta= 11 . Find the value of k