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Question
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, the\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]
Options
- \[- \frac{b}{d}\]
- \[\frac{c}{d}\]
- \[- \frac{c}{d}\]
- \[- \frac{c}{a}\]
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Solution
We have to find the value of `1/alpha + a/beta+1/y`
Given `alpha , beta ,y` be the zeros of the polynomial f(x) = ax3 + bx2 + cx + d
We know that
`alpha ß + beta y + yalpha= - (text{coefficient of x})/(text{coefficient of } x^3)`
`= c/a`
`alphabetay= (-\text{Coefficient of x})/(\text{Coefficient of}x^3)`
`=(-d)/a`
So
`1/alpha + 1/beta+1/y=((c)/a)/(-d/a)`
`1/alpha + 1/beta + 1/y = c/axx(-a/d)`
`1/alpha+ 1/beta+1/y =-c/d`
Hence, the correct choice is `(c)`.
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