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

Answer

The polynomial generated from the given zeros is: $P (x) = 3 x^{3} + 16 x^{2} + 23 x + 6$

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} + 16 x^{2} + 23 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+16x2+23x+6

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

The polynomial generated from the given zeros is: $P (x) = 3 x^{3} + 16 x^{2} + 23 x + 6$