Question

If α and β are two zeroes of a polynomial (fx) = px² – 2x + 3p and α + β = αß, then value of p is ______.

Options

• `(-2)/3`

• `2/3`

• `1/3`

• `(-1)/3`

Answer 1

If α and β are two zeroes of a polynomial (fx) = px² – 2x + 3p and α + β = αß, then value of p is `underlinebb(2/3)`.

Explanation:

Sum of zeroes = α + β

= `(-b)/a`

= `(-(-2))/p` 

= `2/p`

Product of the zeroes = αβ 

= `c/a`

= `(3\cancel(p))/\cancel(p)` 

= 3

a = p; b = –2; c = 3p

`2/p = 3`

2 = 3p

⇒ `p = 2/3`