Home
Class 12
MATHS
The value of lamda such that sum of the ...

The value of `lamda` such that sum of the squares of the roots of the quadratic equation, `x^(2)+(3-lamda)x+2=lamda` had the least value is

A

`5/4`

B

1

C

`15/8`

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
Given, quadratic equation is
`x^(2)+(3+ - lamda)x+2=lamda`
`x^(2)+(3-lamda)x+(2-lamda)=0" "...(i)`
Let Eq. (1) has roots `alpha and beta,` then `alpha+beta,=lamda-3and alpha beta=2-lamda`
`" ""["because"For" ax^(2)+bx+c=0, "sum of roots"=-b/a"and product of roots"=c/a"]"`
Now, `alpha^(2)+beta^(2)=(alpha+beta)^(2)-2alphabeta`
`=(lamda-3)^(2)-2(2-lamda)`
`=lamda^(2)-4lamda+5=(lamda^(2)-4lamda+4)+1=(lamda-2)^(2)+1`
Clearly, `almda^(2)+beta^(2)` will be least when `lamda=2.`
Promotional Banner

Similar Questions

Explore conceptually related problems

Product of the roots of the quadratic equation x^(2)+3x=0 is

The value of a for which the sum of the squares of the roots of the equation x^(2)-(a-2)x-a-1=0 assume the least value is

The real roots of the quadratic equation x^(2)-x-1=0 are ___.

Find the roots of the following quadratic equations x^2-2x-3

Find the sum of the squares of the roots of 3x^3-2x^2+4x+1=0

Find the sum of squares of roots of the equation 2x^4 - 8x^3 + 6x^2 - 3=0

The sum of square of roots of the equation 2x^4+x^2+x+2=0 is :

The equation whose roots are the squares of the roots of the eqation 2x^(2)+3x+1=0 is

If x=9 is one root of the quadratic equation x^(2)-11x+k=0 , then find the value of k.