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

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

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

If x^2+ax+b=0,x^2+bx+a=0 have a common roots then

IF the equations 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 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 x^2+3x +5=0 and ax^(2)+bx +c=0 have common roots / roots and and a,b,c in N , then the minimum value of a +b+c is