Question

If α and β are the zeros of the polynomial f(x) = x 2 + px + q, then a polynomial having is its zero is

a. qx 2 + px + 1
b. x 2 + qx + p
c. x 2 − px + q
d. px 2 + qx + 1​

Answer Step by step

Answer 1

() + +1

α+β= -p, αβ=q

so, the polynomial having 1/α & 1/β as it's zeros.

Sum of zeroes =1/α + 1/β = α + β / αβ = -p/q

Product of zeroes = 1/α × 1/β=1/q

so, the polynomial is

= x2 +p/qx +1/q

=(qx2 + px +1 )

= qx2 +px +1

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