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

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

If ax^2+bx+c =0 and cx^2+bx+a =0 (a,b,cinR) have a common non-real roots,then

If the equations x^2 + 2x + 3 = 0 and ax^2 + bx + + c = 0 have common root, then a : b : c is _____

If (x ^(2) -1) is a factor of ax ^(4) + bx ^(3) + cx ^(2) + dx +e, then show that a + c +e =b +d=0

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

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

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 f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the values of a and b.

if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b