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If α, β Are the Zeros of the Polynomial F(X) = X2 − P(X + 1) − C Such that (α +1) (β + 1) = 0, Then C = - Mathematics

MCQ

If α, β are the zeros of the polynomial f(x) = x2 − p(x + 1) − c such that (α +1) (β + 1) = 0, then c =

Options

  • 1

  • 0

  • -1

  • 2

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Solution

Since `alpha` and `beta` are the zeros of quadratic polynomial

f(x) = x2 − p(x + 1) − c

`f(x)= x^2 - px -p-c`

`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`

`= -(-p/1)`

`= p`

`alphabeta= (\text{Coefficient of x})/(\text{Coefficient of}x^2)`

`= (-p-c)/1`

`= -p-c`

We have 

`0 = (alpha + 1)(beta+1)`

`0=alpha beta + (alpha +beta)+1`

`0 = - cancel(p)-c + cancel(p) +1`

`0 = -c +1`

The value of c is 1.

Hence, the correct alternative is `(a)`

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Q 7 | Page 61
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