Question

If $\alpha \beta \gamma$ are the zeros of the polynomial $f(x)=ax^{3}+bx^{2}+cx+d$, then $\frac{1}{\alpha} \frac{1}{\beta} \frac{1}{\gamma}$=
(a) $-\frac{b}{d}$
(b) $\frac{c}{d}$
(c) $-\frac{c}{d}$
(d) $-\frac{c}{a}$

Answer 1

SOLUTION :  

The correct option is (c) : - c/d .

Given : α,β,γ are the three Zeroes of the cubic polynomial f(x) = ax³ + bx² + cx + d

On comparing with ax³ + bx² + cx + d,

a = a , b= b ,c = c , d = d

Product of the zeroes = - constant term / coefficient of x²

αβγ = - d/a …………(1)

Sum of the product  of its zeroes taken two at a time = coefficient of x / coefficient of x³

αβ + βγ + αγ = c/a ………….(2)

The value of : 1/α + 1/β + 1/γ

= βγ + αγ + αβ / αβγ

= (c/a) / (-d/a)

[From eq 1 & 2 ]

= c/a × - a/d

= - c/d  

Hence, the value of 1/α + 1/β + 1/γ is - c/d .

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

answer (a) is right