Question

A quadratic equation whose roots are ${\sec }^2\alpha$ and $cose{c}^2$ $\alpha$ can be

• A. $x^2-5x+1=0$
• B. $x^2-4x+6=0$
• C. $x^2-5x+5=0$
• D. none of these.

Answer 1

Answer: (C)

If ${\sec }^2\alpha$ and $cose{c}^2\alpha$ are the roots of $x^2+ax+b=0$, then ${\sec }^2\alpha +cose{c}^2\alpha =-a$ and ${\sec }^2\alpha cose{c}^2\alpha =b$
$\Rightarrow -a=b$
$(\because {\sec }^2\alpha cose{c}^2\alpha ={\sec }^2\alpha +cose{c}^2\alpha )$
$\Rightarrow a+b=0$
Also ${\sec }^2\alpha +cose{c}^2\alpha \ge 4$
$\Rightarrow b={\sec }^2\alpha cose{c}^2\alpha \ge 4$
Hence, $x^2-5x+5=0$ can be a quadratic whose roots are $cose{c}^2\alpha$ and $se{c}^2\alpha$.