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SSC CGL 2017 PYQ — Question 75

SSC CGL Tier II Quant - 12/01/2017 • Quantitative Aptitude • Q75

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If x, y, z are the three factors of a​​​​​​3 – 7a – 6, then value of x + y + z will be?

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Correct answer: A

Explanation

  The correct answer is option 1 i.e. 3a

Application

a3 – 7a – 6

⇒ a3 – a – 6a – 6

⇒ a(a2 – 1) – 6(a2 + 1)

⇒ a(a + 1)(a – 1) – 6(a + 1)

⇒ (a + 1) [a(a – 1) – 6)]

⇒ (a + 1) [a2 – a – 6]

⇒ (a + 1) [a2 – 3a + 2a – 6]

⇒ (a + 1) [a(a – 3) + 2(a – 3)]

⇒ (a + 1) (a – 3) (a + 2)

Let x = (a + 1), y = (a – 3) and z = (a + 2)

Hence,

x + y + z = a + 1 + a – 3 + a + 2 = 3a