Question

Ifa and B are the zeroes of the
polynomial f(x) = x^2-X-1 then find the
value of 1/a + 1/B

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Answer 1

Answer:

-1

Step-by-step explanation:

f(x) = x² - x - 1

$As \: \: x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \:$

$so \: \: a \: = \: \frac{1 + \sqrt{5} }{2} \: and \: \: b = \: \frac{1 - \sqrt{5} }{2}$

So, 1/a + 1/b =

$\: \: \: \: \: \frac{2}{1 + \sqrt{5} } + \frac{2}{1 - \sqrt{5} } \\ = \frac{2(1 - \sqrt{5} ) + 2(1 + \sqrt{5}) }{ {1}^{2} - {\sqrt{5}}^{2} } \\ \\ = \frac{ \: \: \: 4}{-4} \\ \\ = \: - 1$

$\: \: \: \: \: \: \: Enjoy !!$

Answer 2

ol thanks to xarmy................

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