The sum and product of zeroes of a quadratic polynomial $p(x)$ are ...

Question

The sum and product of zeroes of a quadratic polynomial $p(x)$ are $\dfrac{-1}{3}$ and $2$ respectively. The polynomial $p(x)$ is :

Accepted Answer

Step 1: A quadratic polynomial with given sum $S$ and product $P$ of zeroes is
$$p(x) = k\left[x^2 - Sx + Pight],\quad k 
eq 0$$
Step 2: $$p(x) = k\left[x^2 + \frac{1}{3}x + 2ight]$$
Step 3: Taking $k = -3$ :
$$p(x) = -3x^2 - x - 6$$
Step 4: Verify for $-3x^2 - x - 6$ :
Sum $= \dfrac{-b}{a} = \dfrac{1}{-3} = \dfrac{-1}{3}$ and Product $= \dfrac{c}{a} = \dfrac{-6}{-3} = 2$. \checkmark

Correct option : (D)

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