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

Answer

The polynomial generated from the given zeros is: $P (x) = 3 x^{3} - 14 x^{2} + 13 x + 6$

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} - 14 x^{2} + 13 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)=3x3−14x2+13x+6

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

The polynomial generated from the given zeros is: $P (x) = 3 x^{3} - 14 x^{2} + 13 x + 6$