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)`

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 .