Question

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

विकल्प

• ${\displaystyle \frac{-2}{3}}$

• ${\displaystyle \frac{2}{3}}$

• ${\displaystyle \frac{1}{3}}$

• ${\displaystyle \frac{-1}{3}}$

Answer 1

If α and β are the zeros of a polynomial f(x) = px² – 2x + 3p and α + β = αβ, then p is ${\displaystyle \underline{\frac{2}{3}}}$.

Explanation:

Given f(x) = px² – 2x + 3p

And, α + β = αβ

Sum of zeroes = Product of zeros

${\displaystyle \frac{-b}{\alpha }=\frac{c}{\alpha }}$

–b = c

Putting values

–(–2) = 3p

2 = 3p

3p = 2

p = ${\displaystyle \frac{2}{3}}$