RRB Group D 22-Sep-2018 Shift 1 Solved Paper

Question : 31 of 100

Marks: +1, -0

3 x^{2}-a x+9=a x^{2}+2 x+5

has only one (repeated) solution, then the positive integral solution of

a

Solution:

Let roots of the equation are

\α

and

\β

(3-a) x^{2}-2 x-a x+4=0

(3-a) x^{2}-x(2+a)+4=0

Standard equation,

a x^{2}+b x+c=0

Sum of roots

=\α+\β={-b}/{a}

\α+\β={(2+a)}/{3-a}

\α\β={c}/{a}

⇒

\α\β={4}/{(3-a)}

According to question,

\α=\β

2 \α={2+a}/{3-a}

......(1)

\α^{2}={4}/{3-a}

......(2)
Solve (1) and (2), a = 2.

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