If `ax^(2)+ bx +c and bx ^(2) + ax + c` have a common factor `x +1` then show that `c=0 and a =b.`

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 the quadratic equations ax^(2)+2bx+c=0 and ax^(2)+2cx+b=0, (b ne c) have a common root, then show that a+4b+4c=0

IF ax^2 + 2cx + b=0 and ax^2 + 2bx +c=0 ( b ne 0) have a common root , then b+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) + ax + b = 0, x^(2) + bx + a = 0 ( a != 0 ) have a common root, then a + b =

IF x^2 +ax+bc=0 and x^2+bx +ca=0 have a common root , then a + b+ c=

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

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