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If 12x2 - ax + 7 = ax2 + 9x + 3 has only one (repeated) solution, then the positive integral solution of a is:
- A2
- B4
- C3
- D5
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CCommunity
12x2 - ax + 7 = ax2 + 9x + 3
⇒ 12x2 - ax + 7 - ax2 - 9x - 3 = 0
⇒ (12 - a)x2 - x(a + 9) + 4 = 0
For only one (repeated) solution, b2 - 4ac = 0
⇒ (a + 9)2 - 16(12 - a) = 0
⇒ a2 + 18a + 81 - 192 + 16a = 0
⇒ a2 + 34a - 101 = 0
⇒ (a + 37)(a - 3) = 0
∴ Positive integral solution of a = 3
⇒ 12x2 - ax + 7 - ax2 - 9x - 3 = 0
⇒ (12 - a)x2 - x(a + 9) + 4 = 0
For only one (repeated) solution, b2 - 4ac = 0
⇒ (a + 9)2 - 16(12 - a) = 0
⇒ a2 + 18a + 81 - 192 + 16a = 0
⇒ a2 + 34a - 101 = 0
⇒ (a + 37)(a - 3) = 0
∴ Positive integral solution of a = 3