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

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

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 c ne 0 and p/(2x)= a/(x+c) + b/(x-c) has two equal roots, then find p.

Let f(x)=ax^(2)+bx+c , g(x)=ax^(2)+qx+r , where a , b , c , q , r in R and a lt 0 . If alpha , beta are the roots of f(x)=0 and alpha+delta , beta+delta are the roots of g(x)=0 , then

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 .

The equation 4ax^2 + 3bx + 2c = 0 where a, b, c are real and a+b+c = 0 has

p^(2)x^(2)+p^(2)x+q=0 the sum of the roots is

If 2 + isqrt3 is a root of x^(3) - 6x^(2) + px + q = 0 (where p and q are real) then p + q is

Let f(x)=ax^(2)+bx+c , g(x)=ax^(2)+px+q , where a , b , c , q , p in R and b ne p . If their discriminants are equal and f(x)=g(x) has a root alpha , then