If and are the zeros of a polynomial and, then p is

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Solution

Q.
If α and β are the zeros of a polynomial $f (x) = p x^{2} - 2 x + 3 p$ and α + β = αβ, then p is

1 $- 2 / 3$

2 $2 / 3$

3 $1 / 3$

4 $- 1 / 3$

Ans.
(2)

Given, $f (x) = p x^{2} - 2 x + 3 p$

Since $α$ and $β$ are the zeroes of the given polynomial.

$∴$ $α + β = - \frac{(- 2)}{p} = \frac{2}{p}, and α β = \frac{3 p}{p} = 3$

$∵$ $α + β = α β$ (given)

$∴$ $\frac{2}{p} = 3 \Rightarrow p = \frac{2}{3}$

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