RRB NTPC Mains or Stage 2 Model Paper 5 with solutions

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Question : 39 of 120

Marks: +1, -0

If for two real constasnts a and b, the expression

ax^3 + 3x^2 – 8x + b

is exactly divisible by (x + 2) and (x – 2), then

a = a, b = 12
a = 12, b = 2
a = 2, b = – 12
a = – 2, b = 12

Solution:

(c)

P(x) = ax^3 + 3x^2 – 8x + b

∴

P (–2) = – 8a + 12 + 16 + b = 0

⇒ – 8a + b + 28 = 0 ...(i)

⇒ P(2) = 8a + 12 – 16 + b = 2

⇒ 8a + b – 4 = 0

...(ii)
By equation (i) + (ii)

2b + 24 = 0 Þ b =24/2 = –12

From equation (i),

– 8a – 12 + 28= 0

⇒ – 8a = – 16 ⇒a = 2

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