Question

If a and B are the zeroes of the polynomial x² - 4x + 1, then the value of a + 1/a
(a) 1
(b) 4
(c) -4
(d) 1/4

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Answer 1

Answer:

$\alpha + \frac{1}{ \alpha } = 4.$

OPTION B IS CORRECT.

Step-by-step explanation:

${x}^{2} + 1 - 4x = 0 \\ \\ divide \: through \: out \: by \: x \\ \\ \frac{ {x}^{2} }{x} + \frac{1}{x} - \frac{4x}{x} = 0 \\ \\ x + \frac{1}{x} = 4 \\ \\ therefore \: \: \: \alpha + \frac{1}{ \alpha } = 4.$