Question

If alpha, beta are zeroes of x^2 - 10x + 5, find the value of
$\alpha { }^{ - 1} + \beta {}^{ - 1} .$

Answer 1

hope it will help you........

Answer 2

Given f(x) = x^2 - 10x + 5.

Given α,β are the zeroes of x^2 - 10x + 5.

Here a = 1, b = -10, c = 5.

Now,

(i)

We know that Sum of zeroes = -b/a

= > α + β = -(-10)/1

= > α + β = 10.

(ii)

We know that Product of zeroes = c/a

= > αβ = (5/1)

= > αβ = 5.

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Now,

$=>\alpha ^{-1} + \beta^{-1}$

$=>\frac{1}{\alpha} + \frac{1}{\beta}$

$=>\frac{\alpha + \beta}{\alpha\beta}$

$=> \frac{10}{5}$

$=> 2$

Hope it helps!