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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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