# If α and β are the zeros of the polynomial f(x) = x2 + px + q, then a polynomial having and is its zeros isA. x2 + qx + pB. x2 – px + qC. qx2 + px + 1D. px2 + qx + 1

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

To find: a polynomial having and 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,

...... (1)

And

...... (2)

Put the values of
α + β  and αβ in (1) and (2) to get,

And

We know equation having 2 zeroes is of form,

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

For a polynomial having and is 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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