Question

For what value of a will the sum of squares of roots of the equation
x2 - (a - 2)x-a-1 = 0 have the least value:
2.5
1
0
6.4​

Answer 1

Answer:

Answer

Correct option is

B

1

Let roots are α and β

from the equation α+β=a−2,αβ=−(a+1)

α

2

+β

2

=(α+β)

2

−2αβ

α

2

+β

2

=(a−2)

2

+2(a+1)=a

2

−2a+6

We have to find minimum value of a

a

2

−2a+6

⇒a

2

−2a+1+5

⇒(a−1)

2

+5

as least value of (a−1)

2

is zero ⇒a−1=0

Therefore, for least value a=1

Hence, option 'B' is correct.