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JEE Main 20199 JanuaryEvening Shift

Exam: JEE Main
Year: 2019
Date: 9 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Quadratic Equation

JEE Main 2019 · 9 January · Evening Shift · Mathematics · Quadratic Equation

The number of all possible positive integral value of α for which...

The number of all possible positive integral value of

\alpha

for which the roots of the quadratic equation

6{x}^{2} - 11x + \alpha = 0

are rational numbers is:

Options

A $5$
B $3$
C $4$
D $2$

Correct answer

B. $3$

Step-by-step solution

For $a{x}^{2} + bx + c = 0$ , we have $D = {b}^{2} - 4ac$

$D = 121 - 24\alpha$
For rational roots, $D$ must be perfect square.
$∴ \alpha = 3, 4, 5$
$∴$ Number of values of $\alpha = 3$

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