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 the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 0 .

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

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 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 ax^2+bx+c=0 and cx^2 + bx+a=0(a,b,c in R) have a common non-real roots, then which of the following is not true ?

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 x^(2)+ax+10=0" and "x^(2)+bx-10=0 have a common root, then a^(2)-b^(2) is equal to

If p(x) = ax^2 + bx + c and Q(x) = -ax^2 + dx +c where ac ne 0 then p(x). Q(x) = 0 has at least …………. Real roots

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