Home
Class 12
MATHS
Let t be a ral number satifying 2t ^(2) ...

Let t be a ral number satifying `2t ^(2) -9t ^(2) + 30 -lamda =0` where `t =x + 1/xand lamda in R.`
If the above cubic has three real and sisinct solutions foe x then exhaustive set of value of `lamda` be :

A

is greater than 9

B

is greater than 11

C

is less than 8

D

is not equal to 10

Text Solution

Verified by Experts

The correct Answer is:
A
a
For `lamda=10impliest_(1)=2,t_(2)gt2` and if `x+1/2x=2impliesx=1` and `x+1//x=t_(20` so there will be two distinct values of `x`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the equation x^4- λx^2+9=0 has four real and distinct roots, then lamda lies in the interval

If t is a real number satisfying the equation 2t^3-9t^2+30-a=0, then find the values of the parameter a for which the equation x+1/x=t gives six real and distinct values of x .

Let alpha, beta be two real roots of the equation cot ^ 2 x - 2 lamda cot x + 3 = 0 , lamda in R . If cot ( alpha + beta ) = (1)/(2) , then value of lamda is :

Let alpha, beta be two real roots of the equation cot ^ 2 x - 2 lamda cot x + 3 = 0 , lamda in R . If cot ( alpha + beta ) = (1)/(2) , then value of lamda is :

2x^2 -4x=t In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ?

If f (x)= tan ^(-1) (sgn (n ^(2) -lamda x+1)) has exactly one point of discontinuity, then the value of lamda can be:

If the difference of the roots of x^(2)-lamdax+8=0 be 2 the value of lamda is

The circle x^2+y^2+4lamdax=0 which lamda in R touches the parabola y^2=8x . The value of lamda is given by

r (x) =3x -7 t (x) =3x + r (x) The function r and t are defined above. What is the value of t (2) ?

A wave is propagating on a long stretched string along its length taken as the positive x-axis. The wave equation is given as y=y_0e^(-(t/T-x/lamda)^(2)) where y_0=4mm, T=1.0s and lamda=4cm .(a) find the velocity of wave. (b) find the function f(t) giving the displacement of particle at x=0. (c) find the function g(x) giving the shape of the string at t=0.(d) plot the shape g(x) of the string at t=0 (e) Plot of the shape of the string at t=5s.