# P If α, β, γ Are the Zeros of the Polynomial F(X) = Ax3 + Bx2 + Cx + D, the 1 α + 1 β + 1 γ = - Mathematics

MCQ

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

• $- \frac{b}{d}$
• $\frac{c}{d}$
• $- \frac{c}{d}$
• $- \frac{c}{a}$

#### 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).

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Q 17 | Page 63