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BITSAT 2024Paper 2

Exam: BITSAT
Year: 2024
Paper: Paper 2
Subject: Mathematics
Chapter: Quadratic Equation

BITSAT 2024 · Paper 2 · Mathematics · Quadratic Equation

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

Rational roots of the equation

2 x^4+x^3-11 x^2+x+2=0

are

Options

A $\frac{1}{2}$ and 2
B $\frac{1}{2}, 2, \frac{1}{4},-2$
C $\frac{1}{2}, 2,3,4$
D $\frac{1}{2}, 2, \frac{3}{4},-2$

Correct answer

A. $\frac{1}{2}$ and 2

Step-by-step solution

Given equation can be reduced to a quadratic equation.

\therefore 2 x^2+x-11+\frac{1}{x}+\frac{2}{x^2}=0\Rightarrow 2

\left(x^2+\frac{1}{x^2}\right)+

\left(x+\frac{1}{x}\right)-11=0

Put

x+\frac{1}{x}=y2\left(y^2-2\right)+y-11=0\Rightarrow 2 y^2+y-15=0\Rightarrow y=-3

and

\frac{5}{2}\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

Only 2nd equation has rational roots as

\mathrm{D}=9

and roots are

\frac{1}{2}

and 2.

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