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`.

lf the quadratic equations x^2+bx+c=0 and bx^2+cx+1=0 have a common root then prove that either b+c+1=0 or b^2+c^2+1=bc+b+c .

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

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

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

If a,b,c in R and equations ax^2 + bx + c = 0 and x^2 + 2x + 9 = 0 have a common root, show that a:b:c=1 : 2 : 9.

Let a, b, c be real numbers such that ax^(2) + bx + c = 0 and x^(2) + x + 1 = 0 have a common root. Statement-1: a = b = c Staement-2: Two quadratic equations with real coefficients cannot have only one imainary root common.

If ax^2 + bx + c = 0 and bx^2 + cx+a= 0 have a common root and a!=0 then (a^3+b^3+c^3)/(abc) is

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

If the equations ax^(2) +2bx +c = 0 and Ax^(2) +2Bx+C=0 have a common root and a,b,c are in G.P prove that a/A , b/B, c/C are in H.P