First slide

Theory of equations

Question

The equation $(a + 2) x^{2} + (a - 3) x = 2 a - 1, a \neq - 2$ has rational roots for

Moderate

A

all rational values of a except a = - 2
B

all real values of a except a= - 2
C

rational values of a> 1/2
D

none of these

Solution

We find that: Sum of the coefficients= 0.
Therefore, $x = 1$ is a rational root of the given equation.
Let the other rational root be a. Then,
Product of the roots $= \frac{2 a - 1}{a + 2}$
$\Rightarrow α \times 1 = \frac{2 a - 1}{a + 2} \Rightarrow α = \frac{2 a - 1}{a + 2}$
Clearly, $a$ is rational for all rational values of $a$ except -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