First slide

Theory of equations

Question

The number of values of a for which equations $x^{3} + ax + 1 = 0 and x^{4} + {ax}^{2} + 1 = 0$ have a common root is

Moderate

A

0
B

1
C

2
D

infinite

Solution

Given equations are
$x^{3} + ax + 1 = 0 or x^{4} + {ax}^{2} + x = 0 (1) and x^{4} + {ax}^{2} + 1 = 0 (2)$
From (1) - (2), we get x = 1. Thus, x = 1 is the common roots.
Hence,
$1 + a + 1 = 0 \Rightarrow a = - 2$

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