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Question

The common root of x2−5x+6=0 and x2−8x+15=0 is the root of x2+4x+q=0 then value of q is

A
21
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B
41
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C
21
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D
41
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Solution

The correct option is C 21
x25x+6=0=(x2)(x3)
Roots are 2 and 3
For x28x+15=0=(x5)(x3)
Roots are 3 and 5
We have common root =3
We know that common root is the root of x2+4x+q=0
Putting x=3 we get 9+12+q=0
q=21

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