First slide

Theory of equations

Question

Rational roots of the equation $2 x^{4} + x^{3} - 11 x^{2} + x + 2 = 0$ are

Moderate

A

$\frac{1}{2} and 2$
B

$\frac{1}{2}, 2, \frac{1}{4}, - 2$
C

$\frac{1}{2}, 2, 3, 4$
D

$\frac{1}{2}, 2, \frac{3}{4}, - 2$

Solution

Given equation can be reduced to a quadratic equation .
$∴ 2 x^{2} + x - 11 + \frac{1}{x} + \frac{2}{x^{2}} = 0$
$\begin{array}{l} \Rightarrow 2 (x^{2} + \frac{1}{x^{2}}) + (x + \frac{1}{x}) - 11 = 0 \\ Put x + \frac{1}{x} = y \\ \Rightarrow 2 (y^{2} - 2) + y - 11 = 0 \\ \Rightarrow 2 y^{2} + y - 15 = 0 \\ \Rightarrow x + \frac{1}{x} = - 3, x + \frac{1}{x} = \frac{5}{2} \\ \Rightarrow x^{2} + 3 x + 1 = 0, 2 x^{2} - 5 x + 2 = 0 \end{array}$
Only 2nd equation has rational roots as D =9 and roots are. $\frac{1}{2}$ and 2.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App