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If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are real and less than 3, then which one of the following is correct ?(a) a < 2 (b) 2 < a < 3 (c) 3 < a < 4 (d) a > 4 |
Answer» (a) a < 2. If the roots of the equation x2 – 2ax + a2 – a – 3 = 0 are real and less than 3, then D ≥ 0 and f (3) > 0. ⇒ 4a2 – 4(a2 + a – 3) ≥ 0 and (3)2 – 2a (3) + a2 + a – 3 > 0 ⇒ a2 – a2 – a + 3 ≥ 0 and 9 – 6a + a2 + a – 3 > 0 ⇒ –a + 3 ≥ 0 and a2 – 5a + 6 > 0 ⇒ a – 3 ≤ 0 and (a – 2) (a – 3) > 0 ⇒ a ≤ 3 and a < 2 or a > 3 ⇒ a < 2. |
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