Question

The value of k for which the roots of equation (x - 1)(x - 5) + k = 0 differ by 2 is​

Answer 1

Answer:

the answer is 3

Step-by-step explanation:

I hope it is right

Answer 2

Answer:

= 3

Step-by-step explanation:

Given(x−5)(x−1)+k=0

⇒x

2 −6x+5+k=0−−−−(1)

It is in the form ax2+bx+c=0

∴a=1,b=−6,c=(5+k)

If α and β are the roots then

α+β=6−−−−(2)

αβ=(5+k)−−−−(3)

and given α−β=2−−−−(4)

Adding(2)and(4)we get

2α=8

⇒α=4−−−−(5)

from(3)and(4)

4+β=6

∴β=2−−−−(6)

∴from (3) , (5) and (6) we get

=5+k=4×2

=5+k=8

=k=8-5

Ans = k=3