Question

If $3 + \sqrt{5}$ be the roots of the equation $3 - \sqrt{5}$, then the equation whose roots are $\sqrt{5}$and $|x|^{2}$ is.

• A. $3|x| + 2 = 0$
• B. $e^{\sin x} - e^{- \sin x} - 4$
• C. $= 0$
• D. $x^{2}$

Answer 1

Answer: (B)

$e^{\sin x} - e^{- \sin x} - 4$

Answer 2

$\mathbf{5}\mathbf{x}^{\mathbf{2}}\mathbf{- 3x - 100 = 0}$ be the roots of $k(6x^{2} + 3) + rx + 2x^{2} - 1 = 0$, then $6k(2x^{2} + 1) + px + 4x^{2} - 2 = 0$ and $2r - p$.

Now required equation whose roots are$x^{2} + px + q = 0$is

$x^{2} + \alpha x + \beta = 0$

⇒$p \neq \alpha$ ⇒ $q \neq \beta$.