ax3-5x2+x+p is divisible by x2-3x+2, find the values of a and p
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ax3-5x2+x+p is divisible by x2-3x+2, find the values of a and p
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Step-by-step explanation:
Solution
Let f(x) = a * x ^ 3 - 5x ^ 2 + x + p
Given, f(x) is divisible by x ^ 2 - 3x + 2 .
f(x) is divisible by (x - 1) and (x - 2) .
f(1) = 0 and f(2) = 0
a + p = 4
8a + p = 18
On solving these equations, we get,
a = p = 2