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If α And β Are the Zeros of the Quadratic Polynomial F(X) = X2 − P (X + 1) — C, Show that (α + 1)(β +1) = 1− C. - CBSE Class 10 - Mathematics

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Question

If α and β are the zeros of the quadratic polynomial f(x) = x2 − p (x + 1) — c, show that (α + 1)(β +1) = 1− c.

Solution

Since α and β are the zeros of the quadratic polynomial f(x) = x2 − p (x + 1) — c

Then

x2 - p(x + 1) - c

x2 - px - p - c

`alpha+beta="-coefficient of x"/("coefficient of "x^2)`

`=(-(-p))/1`

= p

 

`alphabeta="constant term"/("coefficient of "x^2)`

`=(-p-c)/1`

= -p-c

We have to prove that (α + 1)(β +1) = 1 − c

(α + 1)(β +1) = 1 - c

(α + 1)β + (α +1)(1) = 1 - c

αβ + β + α + 1 = 1 - c

αβ + (α + β) + 1 = 1 - c

Substituting α + β = p and αβ = -p-c we get,

-p - c + p + 1 = 1 - c

1 - c = 1 - c

Hence, it is shown that (α + 1)(β +1) = 1 - c

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 2: Polynomials
Ex. 2.10 | Q: 18 | Page no. 35
Solution If α And β Are the Zeros of the Quadratic Polynomial F(X) = X2 − P (X + 1) — C, Show that (α + 1)(β +1) = 1− C. Concept: Relationship Between Zeroes and Coefficients of a Polynomial.
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