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Question

If the equations x2+ax+12=0, x2+bx+15=0 and x2+(a+b)x+36=0 have a common root then the possible values of a,b is (are)

A
a=7
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B
a=7
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C
b=8
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D
b=8
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Solution

The correct options are
B a=7
D b=8
We have x2+ax+12=0 .......(1)
x2+bx+15=0 .......(2)
x2+(a+b)x+36=0 .......(3)
Let the common root be m
So,m will satisfy all three equations
m2+am+12=0 .......(4)
m2+bm+15=0 .......(5)
m2+(a+b)m+36=0 .......(6)
Adding (5) and (6), we get
2m2+(a+b)m+27=0 .......(7)
Subtrating (6) from (7) we get
m29=0
m=3 or m=3(which is not possible)
Put m=3 in eqn(4)
9+3a+12=0
3a+21=0
3a=21
a=213=7
a=7
Put m=3 in eqn(5) we get
9+3b+15=0
3b=24
b=243=8
a=7,b=8


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