A value of b for which the equation x^2+...

A value of `b` for which the equation `x^2+b x-1=0,x^2+x+b=0` have one root in common is `-sqrt(2)` b. `-isqrt(3)` c. `sqrt(2)` d. `sqrt(3)`

`-sqrt(2) `

`-isqrt(3) `

`isqrt(5) `

`sqrt(2)`

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
QUADRATIC EQUATIONS & INEQUATIONS
VMC MODULES ENGLISH|Exercise JEE Advance ( Archive )|20 Videos
QUADRATIC EQUATIONS & INEQUATIONS
VMC MODULES ENGLISH|Exercise Numerical value type of JEE Main|15 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

The value of b for which the equation x^2+bx-1=0 and x^2+x+b=0 have one root in common is (a) -sqrt2 (b) -isqrt3 (c) isqrt5 (d) sqrt2

If one root x^2-x-k=0 is square of the other, then k= a. 2+-sqrt(5) b. 2+-sqrt(3) c. 3+-sqrt(2) d. 5+-sqrt(2)

If a , b ,c real in G.P., then the roots of the equation a x^2+b x+c=0 are in the ratio a. 1/2(-1+isqrt(3)) b. 1/2(1-isqrt(3)) c 1/2(-1-isqrt(3)) d. 1/2(1+isqrt(3))

The set of value of a for which both the roots of the equation x^2-(2a-1)x+a=0 are positie is (A) {(2-sqrt(3))/2} (B) {(2-sqrt(3))/2,(2+sqrt(3))/2} (C) [(2+sqrt(3)/2,oo) (D) none of these

The number of values of a for which equations x^3+a x+1=0 and x^4+a x^2+1=0 have a common root is a) 0 b) 1 c) 2 d) Infinite

If one root of the equation x^2+a x+3=0 is 1, then the other root is (a) 3 (b) -3 (c) 2 (d) -2

If x=1 is a common root of the equations a x^2+a x+3=0 and x^2+x+b=0 , then a b=

If a ,b ,c in R and equations a x^2+b x+c=0 and x^2+2x+3=0 have a common root, then find a : b : c

Let A B C be a triangle such that /_A C B=pi/6 and let a , b and c denote the lengths of the side opposite to A , B ,and C respectively. The value(s) of x for which a=x^2+x+1,b=x^2-1,\and\ c=2x+1 is(are) -(2+sqrt(3)) (b) 1+sqrt(3) (c) 2+sqrt(3) (d) 4sqrt(3)

If the equations ax^2 + bx + c = 0 and x^3 + x - 2 = 0 have two common roots then show that 2a = 2b = c .

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

Let alpha and beta be the roots of the equation x^2-6x-2=0 If an=alpha...
Text Solution
|
The quadratic equation p(x)=0 with real coefficients has purely imagin...
Text Solution
|
The set of all real numbers x for which x^2-|x+2|+x >0 is (-oo,-2) b. ...
Text Solution
|
The number of solution of log4(x-1)=log2(x-3) is :
Text Solution
|
For the equation 3x^2+p x+3=0,p >0, if one of the root is square of th...
Text Solution
|
The equation sqrt((x+1))-sqrt((x-1))=sqrt((4x-1)) has
Text Solution
|
The equation x^((3)/4 (log2x)^2+log2 x -(5)/(4))=sqrt(2) has :
Text Solution
|
The equation x-2//x-1=1-2//x-1 has a. no root b. one root c. two equal...
Text Solution
|
For real x , the function (x-a)(x-b)//(x-c) will assume all real value...
Text Solution
|
The number of real solutions of the equation |x^(2)|-3|x|+2=0 is (a) 3...
Text Solution
|
If x lt 0 , lt 0 , x + y +(x)/4=(1)/(2) and (x+y)((x)/y)=-(1)/(2) th...
Text Solution
|
Let a gt 0, b gt 0 and c lt0. Then, both the roots of the equation ax^...
Text Solution
|
Find the set of all solutions of the equation 2^|y| -|2^(y -1) -1| = 2...
Text Solution
|
Find the set of all s for which (2x)/(2x^(2)+5x+2) gt (1)/(x+10
Text Solution
|
Solve for x :(5+2sqrt(6))^(x^2-3)+(5-2sqrt(6))^(x^2-3)=10.
Text Solution
|
The number of solution (s) for the equation 2logxa+log(ax)a+3log(a^2x)...
Text Solution
|
A value of b for which the equation x^2+b x-1=0,x^2+x+b=0 have one roo...
Text Solution
|
For all ' x^(prime),x^2+2a x+(10-3a)>0, then the interval in which ' a...
Text Solution
|
If the roots of the equation x^2-2a x+a^2-a-3=0 are real and less than...
Text Solution
|
Find all real values of x which satisfy x^2-3x+2>0a n dx^2-2x-4lt=0.
Text Solution
|