Question

The roots α,β of the quadratic equation x²-5x+2(k-5)=0 are such that α-β=3,find the value of k​

Answer 1

Step-by-step explanation:

Given x

2

−5x+3(k−1)=0 α,β are roots is given equation.

α−β=11 __________ (1)

using conditions we have α+β=5

αβ=3(k−1)

now α−β=

α

2

+β

2

−2αβ

=

(α+β)

2

−4αβ

(11)

2

=(α+β)

2

−4αβ

121−25=−12(k−1)⇒

12

96

=1−k

[k=-7]

Hence value of k is -7.