Hi!I am currently training for the mathematical olympiad,and I am stuck at the question below. Please help by writing a solution for me,using simple to understand terms.Thanks!

Let \(a, b, c\) be real numbers. Given the equation for \(\cos x\):
**\[a \cos^2(x )+ b \cos (x) + c = 0\]**
Form a quadratic equation in \(\cos (2x)\) whose roots are the same values of \(x\). Compare the equations in \(\cos x\) and \(\cos (2x)\) for \(a=4, b=2, c=-1\).

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TopNewestHi, since this question is pretty easy I'll just give you the link for the solution to the given problem which is pretty much the same method used by most people .And if you still don't get it , reply here . – Azhaghu Roopesh M · 2 years ago

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– Timothy Wan · 2 years ago

I do not get how they formed the quadratic equation.Can you help to explain?Log in to reply

Now just substitute the values of a , b and c in the given equation and compare the coefficients of both the quadratic equation .

Hope I was of some help . – Azhaghu Roopesh M · 2 years ago

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– Timothy Wan · 2 years ago

Yes!Thank you!Log in to reply

Multiply by 2,2cos^2x will become 1+cos2x, then take the 2bcosx to the right and square both sides – Aviroop Pal · 2 years ago

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