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Question

The value of p for which one root of the quadratic equation (p2−5p+3)x2+(3p−1)x+2=0 is twice as large as the other is

A
23
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B
13
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C
13
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D
23
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Solution

The correct option is D 23
Let y and 2y be the roots of the quadratic equation (p25p+3)x2+(3p1)x+2=0
Sum of roots: y+2y=3p+1p25p+3y=3p+13(p25p+3) ....(1)
Product of roots: 2y2=2p25p+3 ....(2)
Substituting (1) in (2), we get
(3p+13(p25p+3))2=1p25p+3
9p26p+1=9p245p+27
p=23
Ans: D

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