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Question

Find the value of 'a' so that x211x+a=0 and x214x+2a=0 have a common root.


A

0

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B

12

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C

24

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D

48

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Solution

The correct options are
A

0


C

24


x214x+2a=0

x211x+a=0

Let the common root be α

α214a+22a=αa2a=111+14

α28a(1) = αa(2) = 13(3)


α=a3 = 8aa

From (2), (3) From (1), (2)

a224a = 0

a = 0 or 24


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