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If (x + a) is the H.C.F of 2x2 + 5x – 12 and x2 + x – 12 then find thevalue of a.
- A-3
- B-2
- C4
- D5
Answer not set
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0
CCommunity
Given that (x + a)is the HCF of 2x2 + 5x - 12 and x2 + x - 12
∴ Substitute x = - a in the any of the above equations, we get
⇒ 2 × (-a)2 + 5 × (-a) - 12 = 0
⇒ 2a2 - 5a - 12 = 0
⇒ 2a2 - 8a + 3a - 12 = 0
⇒ 2a (a - 4) + 3 (a - 4) = 0
⇒ (2a + 3) (a - 4) = 0
⇒ 2a + 3 = 0 and a - 4 = 0
⇒ a = - 3/2 and a = 4
∴ The value of a is 4
∴ Substitute x = - a in the any of the above equations, we get
⇒ 2 × (-a)2 + 5 × (-a) - 12 = 0
⇒ 2a2 - 5a - 12 = 0
⇒ 2a2 - 8a + 3a - 12 = 0
⇒ 2a (a - 4) + 3 (a - 4) = 0
⇒ (2a + 3) (a - 4) = 0
⇒ 2a + 3 = 0 and a - 4 = 0
⇒ a = - 3/2 and a = 4
∴ The value of a is 4
0
CCommunity
4 Is the correct answer