Home
Class 12
MATHS
If the equations 4x^(2)-x-1=0 and 3x^(2)...

If the equations `4x^(2)-x-1=0` and `3x^(2)+(lambda+mu)x+lambda-mu=0` have a root common, then the rational values of `lambda` and `mu` are

A

`lambda=0`, `mu=(-3)/(4)`

B

`lambda=(-3)/(4)`, `mu=(3)/(4)`

C

`lambda=(-3)/(4)`, `mu=0`

D

`lambda=(-3)/(4)`, `mu=(1)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Roots of `4x^(2)-x-1=0` are irrational.
So, one root common implies both roots are common.
`:. (4)/(3)=(-1)/(lambda+mu)=(-1)/(lambda-mu)=(-2)/(2lambda)=(0)/(2mu)`
So, `lambda=(-3)/(4)`, `mu=0`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

If the equation 4x^(2)-x-1=0 and 3x^(2)+(lambda+mu)x+lambda-mu=0 have a root common,then he rational values of lambda and mu are lambda=(-3)/(4) b.lambda=0 c.mu=(3)/(4) b.mu=0

If x^(2)+x-1=0 and 2x^(2)-x+lambda=0 have a common root then

If the equation x^(2)+2(lambda+1)x+lambda^(2)+lambda+7=0 has only negative roots,then the least value of lambda equals

If the roots of the equation x^(2)+3x+2=0 and x^(2)-x+lambda=0 are in the same ratio then the value of lambda is given by

If the points A(-1, 3, lambda), B(-2, 0, 1) and C(-4, mu, -3) are collinear, then the values of lambda and mu are

If the following equations x+y-3=0,(1+lambda)x+(2+lambda)y-8=0,x-(1+lambda)y+(2+lambda)=0 are consistent then the value of lambda is

If the equation (lambda^(2)-5 lambda+6)x^(2)+(lambda^(2)-3 lambda+2)x+(lambda^(2)-4)=0 is satisfied by more then two values of x then lambda=

Let lambda,mu be such that the equations 4x^(2)-8x+3=0,x^(2)+lambda x-1=0 and 2x^(2)+x+mu=0 may have a common root for each pair of equations but all 3 equations do not have a common root,then mu xx lambda equals

If the points (0,1,-2),(3,lambda,-1) and (mu,-3,4) are collinear,then the value of lambda and mu are given by

If x^(2)+lambda x+1=0, lambda in (-2,2) and 4x^(2)+3x+2c=0 have common root then c+lambda, can be