Question

if alpha and beta are the zeros of the polynomial x2-2x+1 then find 1/alpha+1/beta

Answer 1

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$\huge \boxed{ \sf \orange {\frac{1}{ \alpha } + \frac{1}{ \beta } = 2}}$

Step-by-step explanation:

Q.

If alpha and beta are two zeroes of the polynomial x² - 2x + 1, then find 1/alpha + 1/beta

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Solution -

Let us find the value of alpha and beta (zeroes of polynomial)

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$\sf = > {x}^{2} - 2x + 1 \\ = > \sf {x}^{2} - x - x + 1 \\ = > \sf x(x - 1) - 1(x - 1) \\ = > \sf(x - 1)(x - 1) \\ \sf zeroes = \\ \sf x - 1 = 0 \\ = > \sf x = 1 \\ \\ \sf x - 1 = 0 \\ \sf= > x = 1$

Hence alpha = 1, and beta is also 1

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$\sf \frac{1}{ \alpha } + \frac{1}{ \beta } \\ \\ = > \sf \frac{1}{1} + \frac{1}{1} \\ \\ = > \sf1 + 1 \\ \\ = > 2$

Hence 1/alpha + 1/beta = 2

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hope it helps.