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Question
Find the value k where x-3id a factor of k2x3-kx2+3kx-k.
Find the value k where x-3id a factor of k2x3-kx2+3kx-k.
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Solution
Let f(x) = k²x³ - kx² + 3kx - k.
if (x-3) is a factor of the given problem, then (x-3) it must be zero.
x-3=0
so x=3
f(3) = 0
k²(3)³ - k(3)² + 3k(3) - k = 0
27k² - k = 0
k(27k - 1) = 0
k = 0 or k = 1/27
if (x-3) is a factor of the given problem, then (x-3) it must be zero.
x-3=0
so x=3
f(3) = 0
k²(3)³ - k(3)² + 3k(3) - k = 0
27k² - k = 0
k(27k - 1) = 0
k = 0 or k = 1/27
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