The number of values of the triplet $$(a, b, c)$$ for which $$a\cos 2x + b{\sin ^2}x + c = 0$$ is satisfied by all real $$x$$ is
A.
0
B.
2
C.
3
D.
infinite
Answer :
infinite
Solution :
$$a\left( {1 - 2{{\sin }^2}x} \right) + b{\sin ^2}x + c = 0,\,{\text{i}}{\text{.e}}{\text{., }}\left( {b - 2a} \right){\sin ^2}x + \left( {a + c} \right) = 0.$$
It is an identity if $$b - 2a = 0,a + c = 0.\,{\text{So, }}\frac{a}{1} = \frac{b}{2} = \frac{c}{{ - 1}}.$$
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