Question

If α and β are the zeros of a polynomial f(x) = px² – 2x + 3p and α + β = αβ, then p is ______.

Options

• `(-2)/3`

• `2/3`

• `1/3`

• `(-1)/3`

Answer 1

If α and β are the zeros of a polynomial f(x) = px² – 2x + 3p and α + β = αβ, then p is `underline(bb(2/3)`.

Explanation:

Given f(x) = px² – 2x + 3p

And, α + β = αβ

Sum of zeroes = Product of zeros

`(-b)/α = c/α`

–b = c

Putting values

–(–2) = 3p

2 = 3p

3p = 2

p = `2/3`