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: $P (x) = 3 x^{3} - 16 x^{2} + 23 x - 6$