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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`
Solution
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`
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