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

Consider two quadratic expressions f(x) =ax^2+ bx + c and g (x)=ax^2+px+c,( a, b, c, p,q in R, b != p) such that their discriminants are equal. If f(x)= g(x) has a root x = alpha , then

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

Let f(x)=ax^(5)+bx^(4)+cx^(3)+dx^(2)+ ex , where a,b,c,d,e in R and f(x)=0 has a positive root. alpha . Then,

If f(x) = ax^(2) + bx + c , where a ne 0, b ,c in R , then which of the following conditions implies that f(x) has real roots?

If f(x)=(ax)/b and g(x)=(cx^2)/a , then g(f(a)) equals

If P(x)=ax^2+bx+c , Q(x)=-ax^2+dx+c where ac!=0 then P(x).Q(x)=0 has

Let f(x) = x^3 + ax^2 + bx + c and g(x) = x^3 + bx^2 + cx + a , where a, b, c are integers. Suppose that the following conditions hold- (a) f(1) = 0 , (b) the roots of g(x) = 0 are the squares of the roots of f(x) = 0. Find the value of: a^(2013) + b^(2013) + c^(2013)

Let f(x)=x^(2)+2px+2q^(2) and g(x)=-x^(2)-2qx+q^(2) (where q ne0 ). If x in R and the minimum value of f(x) is equal to the maximum value of g(x) , then the value of (p^(2))/(q^(2)) is equal to

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

Let f(x)=x^(2)+ax+b , where a, b in R . If f(x)=0 has all its roots imaginary, then the roots of f(x)+f'(x)+f''(x)=0 are