The polynomials x3 + ax2 + 4x - 1 and 2x3 - x2 + 7a both leave the same remainder when divided by x-2.
What is the value of a?
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Answer:
a = 1
Step-by-step explanation:
Given,
f(x) = x^3 + a x^2 + 4x - 1
g(x) = 2 x^3 - x^2 + 7a
Given, f(x) & g(x) both leave the same remainder when divided by x-2.
=> f (2) = g (2)
=> (2)^3 + a (2)^2 + 4 (2) - 1 = 2 (2)^3 - (2)^2 + 7a
=> 8 + 4a + 8 - 1 = 16 - 4 + 7a
=> 15 + 4a = 12 + 7a
=> 7a - 4a = 15 - 12
=> 3a = 3
=> a = 3/3
.•. a = 1
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