Xsquare +4aX+3=0, 2Xsquare+3aX-9=0
Find (a) value?
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If x
2
+4ax+3=0 and 2x
2
+3ax−9=0 have a common root, then the value of 'a' is ______.
Answer
Correct option is
A
±3
Let the common root of the equations be p.
Then, p
2
+4ap+3=0 ⇒ 2p
2
+8ap+6=0
and 2p
2
+3ap−9=0
Equating both the equations
2p
2
+8ap+6 = 2p
2
+3ap−9
⇒ 5ap=−15
⇒ ap=−3
Substitute the value of ap in the first equation
Then, p
2
+4(−3)+3=0
⇒ p
2
=9
⇒ p=±3
⇒ a=±1
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