Question

1If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.

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Answer 1

Answer:

p(x) = k(x²+(alpha + beta) x + alpha beta

= 1(x² +(-6)x + 5

=x²-6x+5

Step-by-step explanation:

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Answer 2

Answer:

If α and β are the zeros of the polynomial f(x) = x2 + px + q,

To find: A polynomial having 1 α 1α and 1 β 1β is its zeros is Solution:

f(x) = x2 + px + q

We know, Since α, β are zeroes of given polynomial, ⇒ α + β = – p and αβ = q

Let S and P denote respectively the sum and product of zeroes of the required polynomial,

So, Put the values of α + β and αβ in (1) and (2) to get, ⇒ S = − p q −pq And P = 1 q 1q

We know equation having 2 zeroes is of form,

k (x2 - (sum of zeroes) x + product of zeroes)

For a polynomial having 1 α 1α and 1 β 1βis

its zeros the equation becomes, x2 + p/q x + 1/q = 0 So here we get, g(x) = qx2 + px + 1

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