The quadratic equation whose one root is 1 2 + 5 will be - Vidyadip

MCQ

The quadratic equation whose one root is $\frac{1}{{2 + \sqrt 5 }}$ will be

✓
${x^2} + 4x - 1 = 0$
B
${x^2} + 4x + 1 = 0$
C
${x^2} - 4x - 1 = 0$
D
$\sqrt 2 {x^2} - 4x + 1 = 0$

✓

Answer

Correct option: A.

${x^2} + 4x - 1 = 0$

a
(a) Let $\alpha = \frac{1}{{2 + \sqrt 5 }}$and $\beta = \frac{1}{{2 - \sqrt 5 }}$

Sum of roots $\alpha + \beta = - 4$ and product of roots $\alpha \beta = - 1$

Thus required equation is ${x^2} + 4x - 1 = 0$

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