The polynomials ax^3 + 3x^2 - 13 and 2x^3 - 5x + a are divided by x + 2 if the remainder in each case is the same, find the value of a.
The polynomials ax3 + 3x2 - 13 and 2x3 - 5x + a are divided by x + 2 if the remainder in each case is the same, find the value of a.
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p(x) = ax3 + 3x2 - 13 and q(x) = 2x3 - 5x + a
when p(x) & q(x) are divided by x + 2 = 0 ⇒ x = -2
p (-2) = q(-2)
⇒ a(-2)3 + 3(-2)2 - 13 = 2 (-2)3 - 5(-2) + a
⇒ -8a + 12 - 13 = - 16 + 10 + a
⇒ -9a = - 5
⇒ a = 5/9
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