The polynomial $$\left( {a{x^2} + bx + c} \right)\left( {a{x^2} - dx - c} \right),ac \ne 0,$$ has
A.
four real zeros
B.
at least two real zeros
C.
at most two real zeros
D.
no real zeros
Answer :
at least two real zeros
Solution :
$$\eqalign{
& D = {b^2} - 4ac,D' = {d^2} + 4ac \cr
& \Rightarrow \,\,D + D' = {b^2} + {d^2} > 0 \cr} $$
∴ at least one of $$D, D'$$ is positive.
Releted MCQ Question on Algebra >> Quadratic Equation
Releted Question 1
If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are