Find the polynomial having roots at $- \frac{1}{3}$ , $- 2$ and $3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 3 x^{3} - 2 x^{2} - 19 x - 6$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- \frac{1}{3}$	$3 x + 1$
$- 2$	$x + 2$
$3$	$x - 3$

Step 2: Multiply the factors together:

P (x) = (3 x + 1) \cdot (x + 2) \cdot (x - 3) = 3 x^{3} - 2 x^{2} - 19 x - 6

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Find the polynomial having roots at −31​ , −2 and 3 .

The polynomial generated from the given zeros is: P(x)=3x3−2x2−19x−6

Find the polynomial having roots at $- \frac{1}{3}$ , $- 2$ and $3$ .

The polynomial generated from the given zeros is: $P (x) = 3 x^{3} - 2 x^{2} - 19 x - 6$