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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

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

  Is there an error in this question or solution?
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APPEARS IN

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