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Asked by honey_physics | 09 Sep, 2009, 01:30: PM Expert Answer

Let p(x) = ax3 + 3x2 -bx - 6ax

-1 and -2 are the zeroes of the polynomial

p(-1) = ax3 + 3x2 -bx - 6ax

= 5a + b = -3     ..............(1)

p(-2) = 2a + b = -6     .............(2)

From equation (1) and (2), we get

a = 1 and b = -8

Subsitituting the values in the cubic polynomial p(x)

p(x) = x3 + 3x2 + 2x

Now it is given that (x+1)(x+2) is the factor of the polynomial x3 + 3x2 + 2x

⇒ x3 + 3x2 + 2x = (x+1)(x+2)x

So the thord zero is x = 0

Thanks.

Answered by | 09 Sep, 2009, 03:19: PM
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