\(\displaystyle \mbox{If the equa}\mbox{tion }\, \sqrt{\strut 2\,}\, x^2\, -\, \sqrt{\strut 3\,}\, x\, +\, k\, =\, 0,\, \mbox{ with }\, k\, \mbox{ a constant, has two}\)
\(\displaystyle \mbox{solu}\mbox{tions, }\, \sin(\theta)\, \mbox{ and }\, \cos(\theta),\, \bigg(\, 0\, \leq\, \theta\, \leq\, \dfrac{\pi}{2}\, \bigg),\, \mbox{ then }\, k\, =\, \)\(\displaystyle \fbox{ ?? }\)
How should i start in order to solve this problem? i know the cos sum, sin sum and cos.cos+ sin.sin =1 trig laws, and i realized that we could use the x+ X" = -b/a and x . x " = c/a properties but i dont know how to start, and i tried to substitute the roots for cos or sin by dividing for 2 but i couldnt manage to solve it.
\(\displaystyle \mbox{solu}\mbox{tions, }\, \sin(\theta)\, \mbox{ and }\, \cos(\theta),\, \bigg(\, 0\, \leq\, \theta\, \leq\, \dfrac{\pi}{2}\, \bigg),\, \mbox{ then }\, k\, =\, \)\(\displaystyle \fbox{ ?? }\)
How should i start in order to solve this problem? i know the cos sum, sin sum and cos.cos+ sin.sin =1 trig laws, and i realized that we could use the x+ X" = -b/a and x . x " = c/a properties but i dont know how to start, and i tried to substitute the roots for cos or sin by dividing for 2 but i couldnt manage to solve it.
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