Let
be real numbers. Consider the quadratic equation in
Using the numbers
form a quadratic equation in
whose roots are the same as those of the original equation. Compare the equation in
and
for
,
,
.
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Let $a,b,c$ be real numbers. Consider the quadratic equation in $\cos{x}$ $$a \cos^2{x}+b \cos{x}+c=0.$$ Using the numbers $a,b,c$ form a quadratic equation in $\cos{2x}$ whose roots are the same as those of the original equation. Compare the equation in $\cos{x}$ and $\cos{2x}$ for $a=4$, $b=2$, $c=-1$.
Školjka