Question

If a, B and y are zeroes of the polynomial 6x^3 + 3x^2
- 5x + 1, then find the value of a^-1 + B^-1 + r^-1​

Answer 1

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Answer 2

Answer:

$p(x) = 6 {x}^{3} + 3 {x}^{2} - 5x + 1$

a = 6

b = 3

c = -5

d = 1

Given zeroes are a, B and y.

$let \: zeroes \: are \: ....\alpha .... \beta \: and \: \gamma$

$\alpha \beta + \beta \gamma + \gamma \alpha = \frac{c}{a} = \frac{ - 5}{6}$

$\alpha \beta \gamma = \frac{ - d}{a} = \frac{ - 1}{6}$

According to the question..

$\frac{1 }{ \alpha } + \frac{1}{ \beta } + \frac{1}{ \gamma } = \frac{ \beta \gamma + \alpha \gamma + \alpha \beta }{ \alpha \beta \gamma } = 5$

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