SSC CHSL Model Paper 3

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Question : 41 of 100

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:

P(x) = ax^3 + 3x^2-8x+ b

∴

P (-2 ) = -8 a + 12 + 16 + b = 0

⇒

-8 a + b + 28 = 0

...(i)
⇒

P(2) = 8a+ 12 - 16 + b = 2

⇒

8a + b -4 = 0

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

2b+24 = 0

⇒

b=-24/2=-12

From equation (i),

- 8 a - 12 + 28= 0

⇒

-8a =-16⇒a=2

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