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

• \[- \frac{b}{d}\]
• \[\frac{c}{d}\]
• \[- \frac{c}{d}\]
• \[- \frac{c}{a}\]

Answer 1

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)`.