Question

the roots of alpha and beta of a quadratic equation x^3-5x+2(k-1)=0 are such that alpha minus alpha beta =1.Find the value of k​

Answer 1

Answer:

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.

Step-by-step explanation: