Home
Class 12
MATHS
A value of b for which the equations : ...

A value of b for which the equations :
`x^(2) + bx - 1= 0, x^(2) + x + b = 0`
Have one root in common is :

A

`-sqrt(2)`

B

`-isqrt(3),i=sqrt(-1)`

C

`isqrt(5),i=sqrt(-1)`

D

`sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `alpha` be the common root.
Then `alpha^(2)+b aopha-1=0` and `alpha^(2)+alpha+beta=0`
implies|(1,b),(1,1)|xx|(b,-1),(1,b)|=|(-1,1),(b,1)|^(2)`
`implies(1-b)(b^(2)+1)=(-1-b)^(2)`
`impliesb^(3)+3b=0`
`:.b=0, isqrt(3),-isqrt(3)` where `i=sqrt(-1)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The value of 'a' for which the equation x^(3) + ax + 1 = 0 and x^(4) + ax^(2) + 1 =0 has a common root is :

Find the value of lamda so that the equations x^(2)-x-12=0 and lamdax^(2)+10x+3=0 may have one root in common. Also, find the common root.

The quadratic equations : x^(2) - 6x + a = 0 and x^(2) - cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. then the common root is :

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 :

The positive value of K for which both the equations x^(2)+Kx+64=0 and x^(2)-8x+K=0 have real roots, is

If the equations : 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 a x^(2)+2 b x+c-0 and a x^(2)+2 c x+b=0 , b ne c have a common root, then (a)/(b+c)=

If a,b,c are in G.P.L, then the equations ax^(2) + 2bx + c = 0 0 and dx^(2) + 2ex+ f = 0 have a common root if ( d)/( a) , ( e )/( b ) , ( f )/( c ) are in :

If each pair of the three equations x^(2)+ax+b=0, x^(2)+cx+d=0 and x^(2)+ex+f=0 has exactly one root in common then show that (a+c+e)^(2)=4(ac+ce+ea-b-d-f )

The value of b for which the equation 2 log_(1//25)(bx+28)=- log_(5) (12-4x-x^(2)) has coincident roots is