Find the condition on `a , b ,c ,d` such that equations `2a x^3+bx^2+c x+d=0a n d 2ax^2+3b x+4c=0` have a common root.

If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, then

Find the condition that the roots of the equation ax^3+bx^2+cx+d=0 are in A.P.

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

Determine the values of m for which equations 3x^2+4m x+2=0a n d2x^2+3x-2=0 may have a common root.

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 a ,b ,c be the sides of A B C and equations a x^2+b x+c=0a n d5x^2+12x+13=0 have a common root, then find /_Cdot

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

Find the condition that the roots of cubic equation x^3+ax^2+bx+c=0 are in the ratio p : q : r .

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=