Question

If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d, then (1/α) + (1/β) + (1/γ) =
A. -b/d
B. c/d
C. -c/d
D. -c/a

Answer 1

(c) -c/d

Step-by-step explanation:

$f(x)=ax^3+bx^3+cx+d$

let the $\alpha ,\beta,$ and $\gamma$ are the zeroes of the polynomial

$\alpha+\beta+\gamma=\frac{-b}{a} \\\alpha\beta\gamma=\frac{-d}{a}\\\alpha\beta+\beta\gamma+\gamma\alpha=\frac{c}{a}$

According to question

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

Now, take LCM

$\frac{\alpha\beta+\beta\gamma+\gamma\alpha}{\alpha\beta\gamma}$  

put the value of  $\\\alpha\beta+\beta\gamma+\gamma\alpha$  and  $\alpha \beta \gamma$

$\frac{c}{a} \div \frac{-d}{a}$

$\frac{c}{a}\times\frac{-a}{d}\\\\= \frac{-c}{d}$

Answer 2

Answer:

option c -c/d

Step-by-step explanation: