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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $a$ , $b$ , $c$ are $p^{th}$ , $q^{th}$ , $r^{th}$ terms of an $H.P.$ and $\vec u = \left( {q-r} \right)\hat i + \left( {r - p} \right)\hat j + \left( {p - q} \right)\hat k$ ,$\vec \upsilon = \frac{{\hat i}}{a} + \frac{{\hat j}}{b} + \frac{{\hat k}}{c}$ then

Let $A + 2B =$ $\left[ {\begin{array}{*{20}{c}}1&2&0\\6&{ - 3}&3\\{ - 5}&3&1 \end{array}} \right]$ and $2A - B =$ $\left[ {\begin{array}{*{20}{c}}2&{ - 1}&5\\ 2&{ - 1}&6\\0&1&2\end{array}} \right]$ then $Tr (A) - Tr (B)$ has the value equal to

$\alpha=\sin 36^{\circ}$ is a root of which of the following equation

Let $A$ be a $2 \times 2$ matrix of the form $A=\left[\begin{array}{ll}a & b \\ 1 & 1\end{array}\right]$, where $a, b$ are integers and $-50 \leq b \leq 50$. The number of such matrices $A$ such that $A^{-1}$, the inverse of $A$, exists and $A^{-1}$ contains only integer entries is

The roots of the equation $\left| {\,\begin{array}{*{20}{c}}0&x&{16}\\x&5&7\\0&9&x\end{array}\,} \right| = 0$ are

If the points $(x + 1,\,2),\;(1,x + 2),\;\left( {\frac{1}{{x + 1}},\frac{2}{{x + 1}}} \right)$ are collinear, then x is

Sum of the series $1\cdot 2015 + 2\cdot 2014 + 3\cdot 2013 +.....2015\cdot 1$ is equal to :-

If $\alpha $ and $\beta $, $\alpha $ and $\gamma $, $\alpha $ and $\delta $ are the roots of the equations $a{x^2} + 2bx + c = 0$, $2b{x^2} + cx + a = 0$ and $c{x^2} + ax + 2b = 0$ respectively, where $a,b$ and $c$ are positive real numbers, then $\alpha + {\alpha ^2}$=

If $8=3+\frac{1}{4}(3+p)+\frac{1}{4^2}(3+2 p)+\frac{1}{4^3}(3+3 p)+\ldots \infty,$ then the value of $p$ is

A circle in inscribed in an equilateral triangle of side of length $12$. If the area and perimeter of any square inscribed in this circle are $\mathrm{m}$ and $\mathrm{n}$, respectively, then $m+n^2$ is equal to