If the equation `x^2+b x-a=0"and" x^2-a x+b=0` have a common root, then a.`a+b=0` b. `a=b` c. `a-b=1` d. `a+b=1`

If the equations a x^2+b x+c=0a n dx^3+3x^2+3x+2=0 have two common roots, then a. a=b=c b. a=b!=c c. a=-b=c d. none of these

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

For a ne b , if the equation x^(2)+ax+b=0" and "x^(2)+bx+a=0 have a common root, then the value of a+b=

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

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

If a ,b ,c in R and equations a x^2+b x+c=0a n dx^2+2x+9=0 have a common a rot, then find a : b : c dot

If the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 0 .

If the quadratic equations 3 x^(2)+a x+1=0 and 2 x^(2)+b x+1=0 have a common root, then the value of the expression 5 a b-2 a^(2)-3 b^(2) is

If the equation a x^2+b x+c=0,a ,b ,c , in R have none-real roots, then a. c(a-b+c)>0 b. c(a+b+c)>0 c. c(4a-2b+c)>0 d. none of these

If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots and the other roots of the second equation is the reciprocal of the other roots of the first, then (2-2b)^2 . a. 36p a(q-b)^2 b. 18p a(q-b)^2 c. 36b q(p-a)^2 d. 18b q(p-a)^2