Home
Class 12
MATHS
If the equations x^(2)+2lambdax+lambda^(...

If the equations `x^(2)+2lambdax+lambda^(2)+1=0`, `lambda in R` and `ax^(2)+bx+c=0` , where `a`, `b`, `c` are lengths of sides of triangle have a common root, then the possible range of values of `lambda` is

A

`(0,2)`

B

`(sqrt(3),3)`

C

`(2sqrt(2),3sqrt(2))`

D

`(0,oo)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `(x+lambda)^(2)+1=0` has clearly imaginery roots
So, both roots of the equations are common
`:. (a)/(1)=(b)/(2lambda)=(c )/(lambda^(2)+1)=k`(Say)
Then `a=k`, `b=2lambdak`, `c=(lambda^(2)+1)k`
As `a`, `b`, `c` are sides of triangle
`a+b gt implies 2lambda+1 gt lambda^(2)+1implieslambda^(2)-2lambda lt 0`
`implies lambda in (0,2)`
The other conditions also imply same relation.
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)+2x+3=0 and ax^(2)+bx+c=0, a,b,c in R have a common root, then a:b:c is

If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, then

If in any triangle, the area DeltaABC le(b^(2)+c^(2))/(lambda) , then the largest possible numerical value of lambda is

The equations x^2 +3x+5=0 and ax^2+bx+c=0 have a common root. If a,b,c in N then the least possible values of a+b+c is equal to

For a ne b , if the equation x^(2)+ax+b=0" and "x^(2)+bx+a=0 have a common root, then the value of a+b=

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__________.

The common root of the equation x^(2) - bx + c = 0 and x^(2) + b x - a= 0 is ………..

If ax^(2)+bx+c=0 , a ne 0 , a , b , c in R has distinct real roots in (1,2) , then a and 5a+2b+c have

If a x^(2)+b x+c=0 and b x^(2)+c x+a=0, a, b, c ne 0 have a common root, then value of ((a^(3)+b^(3)+c^(3))/(a b c))^(2) is