Quadratic EquationHard
Question
The set of values of ' a ' for which the equation $\cos^{4}x - \sin^{4}x + cos2x + a^{2} + a = 0$ will have atleast one real solution is
Options
A.$\lbrack - 2,1\rbrack$
B.$\lbrack - 1,2\rbrack$
C.$\lbrack - 1,1\rbrack$
D.$\lbrack 1,2\rbrack$
Solution
$- 2cos2x = a^{2} + a$
For equation to have solution
$$\begin{matrix} & - 2 \leq a^{2} + a \leq 2 \\ \Rightarrow & a^{2} + a - 2 \leq 0 \\ \Rightarrow & a \in \lbrack - 2,1\rbrack \end{matrix}$$
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