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JEE Main 2008

Exam: JEE Main
Year: 2008
Subject: Mathematics
Chapter: Quadratic Equation

JEE Main 2008 · Mathematics · Quadratic Equation

The quadratic equations x^2-6 x+a=0 and x^2-c x+6=0 have one root...

The quadratic equations

x^2-6 x+a=0

and

x^2-c x+6=0

have one root in common. The other roots of the first and second equations are integers in the ratio

4: 3

. Then the common root is

Options

A1
B4
C3
D2

Correct answer

D. 2

Step-by-step solution

Let

\alpha

and

4 \beta

be roots of

x^2-6 x+a=0

and

\alpha, 3 \beta

be the roots of

x^2-c x+6=0

, then

\alpha+4 \beta=6

and

4 \alpha \beta=a

\alpha+3 \beta=c

and

3 \alpha \beta=6

. We get

\alpha \beta=2 \Rightarrow a=8

So the first equation is

x^2-6 x+8=0 \Rightarrow x=2,4

If

\alpha=2

and

4 \beta=4

then

3 \beta=3

If

\alpha=4

and

4 \beta=2

, then

3 \beta=3 / 2 \quad

(non-integer)

\therefore

common root is

x=2

.

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