If `x^(2)+bx+c=0, x^(2)+cx+b=0 (b ne c)` have a common root, then show that `b+c+1=0`

If x^(2) + ax + b = 0, x^(2) + bx + a = 0 ( a != 0 ) have a common root, then a + b =

If x^(2)+ax+b=0 and x^(2)+bx+a=0,(a ne b) have a common root, then a+b is equal to

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

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

Suppose the that quadratic equations ax^(2)+bx+c=0 and bx^(2)+cx+a=0 have a common root. Then show that a^(3)+b^(3)+c^(3)=3abc .

If x^2+a x+bc=0 a n d x^2+b x+c a=0(a!=b) have a common root, then prove that their other roots satisfy the equation x^2+c x+a b=0.

If ax^(2)+bx+c=0andbx^(2)+cx+a=0 have a common root then the relation between a,b,c is

If the quadratic equation ax^(2) + 2cx + b = 0 and ax^(2) + 2x + c = 0 ( b != c ) have a common root then a + 4b + 4c is equal to

If x^2+a x+b=0a n dx^2+b x+c a=0(a!=b) have a common root, then prove that their other roots satisfy the equation x^2+c x+a b=0.

If ax^(2)+bx+c=0 and bx^(2)+cx+a=0 have a common root, prove that a+b+c=0 or a=b=c .