Let a,b,c be the sides of a triangle. No...

Let a,b,c be the sides of a triangle. Now two of them are equal to `lamda epsilon R`. If the roots of the equation `x^(2)+2(a+b+c)x+3lamda(ab+bc+ca)=0` are real then

`lambda lt (4)/(3) `

`lambda gt(5)/(3) `

`lambda in ((4)/(3),(5)/(3))`

`lambda in ((1)/(3),(5)/(3))`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

QUADRATIC EQUATIONS & INEQUATIONS
VMC MODULES ENGLISH|Exercise JEE Main ( Archive ) (Fill in the blanks )|3 Videos
PROPERTIES OF TRIANGLE
VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|50 Videos
QUIZ
VMC MODULES ENGLISH|Exercise MATHEMATICS|30 Videos

Similar Questions

Explore conceptually related problems

Let a,b,c be the sides of a triangle. No two of them are equal and lambda in R If the roots of the equation x^2+2(a+b+c)x+3lambda(ab+bc+ca)=0 are real, then (a) lambda 5/3 (c) lambda in (1/5,5/3) (d) lambda in (4/3,5/3)

Let a, b, c be the sides of a triangle . No two of them are equal and λ∈R . If the roots of the equation x ^2+2(a+b+c)x+3λ(ab+bc+ca)=0 are real, then

Let a, b, c be the lengths of the sides of a triangle (no two of them are equal) and k in R .If the roots of the equation x^2 + 2(a+b+c)x+6k(ab+bc+ac)=0 are real, then:

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,b,c will be in

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c .

If a, b, c are real and a!=b , then the roots ofthe equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :

If a,b, cinR , show that roots of the equation (a-b)x^(2)+(b+c-a)x-c=0 are real and unequal,

Find the values of lamda and mu if both the roots of the equation (3lamda+1)x^(2)=(2lamda+3mu)x-3 are infinite.

VMC MODULES ENGLISH-QUADRATIC EQUATIONS & INEQUATIONS -JEE Advance ( Archive )

Let alpha, beta be the roots of the equationpx^(2)+qx+r=0, p!=0. If p,...
Text Solution
|
Let p and q real number such that p!= 0,p^3!=q and p^3!=-q. if alpha a...
Text Solution
|
Let a,b,c be the sides of a triangle. Now two of them are equal to lam...
Text Solution
|
If alpha and beta are the roots of the equation x^2+ax+b=0 and alpha^4...
Text Solution
|
The sum of all real values of x satisfying the equation (x^(2) -5x+5)...
Text Solution
|
Let a and b are the roots of the equation x^2-10 xc -11d =0 and those...
Text Solution
|
If alpha,beta are the roots of a x^2+b x+c=0,(a!=0) and alpha+delta,be...
Text Solution
|
If one root of the quadratic equation ax^(2) + bx + c = 0 is equal ...
Text Solution
|
If alpha,beta are roots of x^2+-p x+1=0a n dgamma,delta are the roots ...
Text Solution
|
If alpha,beta are roots of x^2+-p x+1=0a n dgamma,delta are the roots ...
Text Solution
|
If a in R and the equation =-3(x-[x])^(2)+2(x-[x])+a^(2)=0 (where [x...
Text Solution
|
If x^(2) + (a - b) x + (1 - a - b) = 0, where a , b in R , then find ...
Text Solution
|
Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alphaa n dbet...
Text Solution
|
The smallest value of k for which both roots of the equation x^(2)-8kx...
Text Solution
|
Let a, b, c be real numbers, a != 0. If alpha is a zero of a^2 x^2+bx...
Text Solution
|
Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,...
Text Solution
|
Let (x(0), y(0)) be the solution of the following equations: (2x)^("...
Text Solution
|
If 3^(x)=4^(x-1), then x is equal to
Text Solution
|
The value of 6+ log(3//2) (1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sq...
Text Solution
|
The largest interval for whichx^(12)+x^9+x^4-x+1>0 -4<xlt=0 b. 0<x<1 ...
Text Solution
|