Question

If x²+4ax+3=0 and 2x²+3ax-9=0 have a common root then the value of a is?​

Answer 1

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ANSWER

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Let the common root of the equations be p.

• Then, p 2+4ap+3=0
• ⇒ 2p2+8+6=0 and 2p2+3ap−9=0

Equating both the equation

• 2p 2+8ap+6=2p2+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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Answer 2

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Let the common root be m. Put in the equations;

m² + 4am + 3 = 0 --------------(1)

2m² + 3am - 9 = 0 --------------(2)

multiply equation (1) by 2

2m² + 8am + 6 = 0 -------------(3)

(note that equation 1 and 3 are the same)

subtract (2) from (3); you will get

(2m² + 8am + 6) - (2m² + 3am - 9) = 0

⇒ 5am + 15 = 0

⇒ 5am = -15

⇒ m =

from equation (1),