(C) Given $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$Squaring both sides,we get $x^2 = 2 + \sqrt{2 + \sqrt{2 + \dots}}$Since the expression inside th

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(C) Given $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$Squaring both sides,we get $x^2 = 2 + \sqrt{2 + \sqrt{2 + \dots}}$Since the expression inside the square root is $x$,we can write $x^2 = 2 + x$Rearranging the terms,we get $x^2 - x - 2 = 0$Factoring the quadratic equation: $(x - 2)(x + 1) = 0$This gives $x = 2$ or $x = -1$Since the square root of a positive number must be positive,$x$ cannot be $-1$.Therefore,$x = 2$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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The value of $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$ is

A
$-1$
B
$1$
C
$2$
D
$3$

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4-2.Quadratic Equations and Inequations

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Solution of quadratic equations and Nature of roots

Let $a$ be an integer such that all the real roots of the polynomial $2x^{5}+5x^{4}+10x^{3}+10x^{2}+10x+10$ lie in the interval $(a, a+1)$. Then,$|a|$ is equal to ...... .

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If $\frac{1+\sqrt{3}i}{2}$ is a root of the equation $x^4-x^2+x-1=0$,then its real roots are:

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Let $f(x) = ax^{2} + bx + c$ be such that $f(1) = 3$,$f(-2) = \lambda$,and $f(3) = 4$. If $f(0) + f(1) + f(-2) + f(3) = 14$,then $\lambda$ is equal to...

DifficultJEE MAIN 2022

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If the equation $x^5-3x^4-5x^3+27x^2-32x+12=0$ has repeated roots,then the prime number that divides the non-repeated root of this equation is

MediumAP EAMCET 2017

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If the absolute difference between the roots of the equation $x^2 + px + 3 = 0$ is $\sqrt{p}$,then $p = ......$

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The value of $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$ is

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