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1.2.8 Algebra and Functions

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Question 51

Given that

f(x)=2x3−5x2+8x+k f(x) = 2x^3 - 5x^2 + 8x + k f(x)=2x3−5x2+8x+k

where kkk is a constant.

Given that (2x−1)(2x - 1)(2x−1) is a factor of f(x)f(x)f(x),

a.

use the factor theorem to show that k=−3k = -3k=−3.

[3]
b.

Hence show that the equation f(x)=0f(x) = 0f(x)=0 has only one real root.

[4]

1.2.8 Algebra and Functions Questions

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