Question

If one root of a quadratic equation is $\frac{1}{2 + \sqrt{5}}$, then the equation is

• A. $x^{2} + 4x + 1 = 0$
• B. $x^{2} + 4x - 1 = 0$
• C. $x^{2} - 4x + 1 = 0$
• D. None of these

Answer 1

Answer: (B)

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

Answer 2

Given root $= \frac{1}{2 + \sqrt{5}} = \frac{2 - \sqrt{5}}{- 1} = - 2 + \sqrt{5}$,

∴ other root$= - 2 - \sqrt{5}$

Again, sum of roots = – 4 and product of roots = – 1. The required equation is $x^{2} + 4x - 1 = 0$