Home
Class 12
MATHS
If the quadratic equation x^(2)-36x+lamb...

If the quadratic equation `x^(2)-36x+lambda=0` has roots `alpha` and `beta` such that `alpha`, `beta in N` and `(lambda)/(5) cancel in Z` and `lambda` assumes minimum possible value then `(sqrt(alpha+2)sqrt(beta+2))/(|alpha-beta|)` is equal to

A

`(3)/(8)`

B

`(3)/(16)`

C

`(sqrt(111))/(34)`

D

`(sqrt(111))/(17)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `x^(2)-36x+lambda=0`
`:. Lambda=36x-x^(2)`
`alpha=1`, `lambda=5`, `beta=35` (rejected)

`:.alpha=2`, `lambda=68`, `beta=34` or `alpha=34`, `beta=2`
`:. (sqrt(36)sqrt(4))/(32)=(3)/(8)`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

IF cot ( alpha + beta ) =0 then sin ( alpha + 2 beta ) is equal to

If x^(2)+px+q=0 has the roots alpha" and "beta , then the value of (alpha-beta)^(2) is equal to

If tan alpha and tan beta are the roots of x^2 + ax +b =0 then (sin(alpha+beta))/(sin alpha sin beta) is equal to

In a quadratic equation with roots alpha and beta where alpha+beta=-4 and alpha beta=-1 , then required equation is ……………

If tan alpha and tan beta are the roots of x^(2) + ax + b = 0, then (sin (alpha + beta))/(sin alpha sin beta) is equal to

If roots alpha, beta of the equation (x^(2)-bx)/(ax-c)=(lambda-1)/(lambda+1) are such that alpha+ beta=0 , then the value of lambda is

The roots of the equation 2x^(2)-7x+5=0 are alpha and beta . Without solving the root find (alpha)/(beta)+(beta)/(alpha)

The roots of the equation 2x^(2)-7x+5=0 are alpha and beta . Without solving the root find (1)/(alpha)+(1)/(beta)

The roots of the equation 2x^(2)-7x+5=0 are alpha and beta . Without solving the root find (alpha+2)/(beta+2)+(beta+2)/(alpha+2)