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JEE Main 2003

Exam: JEE Main
Year: 2003
Subject: Mathematics
Chapter: Quadratic Equation

JEE Main 2003 · Mathematics · Quadratic Equation

The value of ' a ' for which one root of the quadratic equation...

The value of '

a

' for which one root of the quadratic equation \left(a^2-5 a+3\right) x^3+(3 a-1) x+2=0 is twice as large as the other is

Options

A $-\frac{1}{3}$
B $\frac{2}{3}$
C $-\frac{2}{3}$
D $\frac{1}{3}$

Correct answer

B. $\frac{2}{3}$

Step-by-step solution

3 \alpha=\frac{1-3 a}{a^2-5 a+3} \& 2 \alpha^2=\frac{2}{a^2-5 a+3}

2

\left[\frac{1}{9} \frac{(1-3 a)^2}{

\left(a^2-5 a+3\right)^2}\right]=\frac{2}{a^2-5 a+3}

\frac{(1-3 a)^2}{\left(a^2-5 a+3\right)}=9

or

9 a^2-6 a+1

=9 a^2-45 a+27

or

39 a=26

or

a=\frac{2}{3}

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