Say I have an equation, $\sqrt 2 x^2 - \sqrt 3 x + k = 0$, $k$ is a constant and there are 2 solutions $\sin \theta$ and $\cos\theta$ in the interval $0\le \theta \le \pi/2$.
What is the value of $k$?
How should I view this question? Equaling two equations where one is $f(x) = \sin\theta$ and another $f(x) = \cos\theta$? :p
It'd be great if someone could be of guidance.
$$\sqrt2x^2-\sqrt3x+k=0$$
We have $$\sin\theta+\cos\theta=\dfrac{\sqrt3}{\sqrt2}\ \ \ \ (1)$$
$$\sin\theta\cos\theta=\dfrac k{\sqrt2}\ \ \ \ (2)$$
Take the square of $(1)$
Can you take it from here?