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Anika [276]
1 year ago
12

The polynomial x^3-kx^2+kx+2 has a factor of (x-2). What is the value of k?

Mathematics
1 answer:
laiz [17]1 year ago
5 0

\text{Let}~ f(x) = x^3-kx^2 +kx +2.\\\\\text{If}~ x-2~ \text{is a factor of}~ f(x)~ \text{then,}\\ \\f(2) =0\\\\\implies 2^3-k\cdot 2^2 +2k+2 =0\\\\\implies -4k+2k+8+2=0\\\\\implies 10-2k=0\\\\\implies 2k =10\\\\\implies k= \dfrac{10}2 = 5\\\\\\\text{Hence, the value of k is 5.}

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\text{Number of students who prefer rap}=s=\dfrac{1}{4}\times420\\\Rightarrow s=105

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