Home
Class 12
MATHS
If the equation 4x^2-x-1=0a n d3x^2+(lam...

If the equation `4x^2-x-1=0a n d3x^2+(lambda+mu)x+lambda-mu=0` have a root common, then the rational values of `lambdaa n dmu` are a.`lambda=(-3)/4` b. `lambda=0` c. `mu=3/4` b.`mu=0`

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 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 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 equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a common positive root, then find the values of aa n dbdot

If the equation |x^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distinct solutions then lambda is equal to

If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two parallel straight lines, then prove that lambda=mudot

If the lines 3x^(2)-4xy +y^(2) +8x - 2y- 3 = 0 and 2x - 3y +lambda = 0 are concurrent, then the value of lambda is

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

If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+c

If the equations a x^2+b x+c=0a n dx^3+3x^2+3x+2=0 have two common roots, then a. a=b=c b. a=b!=c c. a=-b=c d. none of these

If the quadratic equations 3 x^(2)+a x+1=0 and 2 x^(2)+b x+1=0 have a common root, then the value of the expression 5 a b-2 a^(2)-3 b^(2) is

If cos^(-1)lambda+cos^(-1)mu+cos^(-1)gamma=3pi, then find the value of lambdamu+mugamma+gammalambda