Question
If one zero of the polynomial $x^2 - 4x + 1$ is $\big(2+\sqrt3\big),$ write the other zero.
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Answer
Given equation is $x^2 - 4x + 1$Let the other root be $\alpha.$
Sum of the roots $=\frac{-(-4)}{1}$
$\Rightarrow\alpha+\big(2+\sqrt3\big)=4$
$\Rightarrow\alpha=4-2-\sqrt3$
$\Rightarrow\alpha=2-\sqrt3$
Sum of the roots $=\frac{-(-4)}{1}$
$\Rightarrow\alpha+\big(2+\sqrt3\big)=4$
$\Rightarrow\alpha=4-2-\sqrt3$
$\Rightarrow\alpha=2-\sqrt3$
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