P(x)=x4−3x3+kx2−6x+14𝑃(𝑥)=𝑥4−3𝑥3+𝑘𝑥2−6𝑥+14, where k is an unknown real number.If (x−2)(𝑥−2) is a factor of this polynomial, what is the value of k?
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Solution 1
Given that (x-2) is a factor of the polynomial, we can use the Factor Theorem which states that a polynomial f(x) has a factor (x-a) if and only if f(a) = 0.
So, if (x-2) is a factor of P(x), then P(2) = 0.
Substitute x = 2 into the polynomial:
P(2) = (2)^4 - 3*(2)^3 + k*(2)^2 - 6*2 + 14 = 0 P(2) Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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P(x)=x4−3x3+kx2−6x+14𝑃(𝑥)=𝑥4−3𝑥3+𝑘𝑥2−6𝑥+14, where k is an unknown real number.If (x−2)(𝑥−2) is a factor of this polynomial, what is the value of k?
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