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Formation of a Quadratic Equation From It's Roots

If α and β ar...

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.

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Solution

Since and are the zeros of the quadratic polynomial

Then

=

=

We have to prove that

Substituting and we get,

Hence, it is shown that.

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α, β

are the zeros of polynomial

f (x) = x^{2} - p (x + 1) - c

(α + 1) (β + 1) =

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

(a) c − 1
(b) 1 − c
(c) c
(d) 1 + c

Q. If α and β are the zeros of the quadratic polynomial f(x) = x² − 2x + 3, find a polynomial whose roots are (i) α + 2, β + 2 (ii)

\frac{α - 1}{α + 1}, \frac{β - 1}{β + 1}

α, β

are zeros of polynomial

x^{2} - p (x + 1) - k

(α + 1) (β + 1) = 6

, then value of k is?

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Formation of a Quadratic Equation From It's Roots

Standard X Mathematics

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