Find a quadratic polynomial with rational coefficients whose one zero is $\sqrt{5} - 2$ .

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Solution

If one root is $\sqrt{5} - 2$
then by rule of quadratic equation
other root is $\sqrt{5} + 2$
$∴$ Quadratic equation $= [x - (\sqrt{5} - 2) [x - (\sqrt{5} + 2)]] = x^{2} - (2 \sqrt{5}) x + 1$

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