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

Answer

The polynomial generated from the given zeros is: $P (x) = 3 x^{2} - 7 x + 2$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x - 2) \cdot (3 x - 1) = 3 x^{2} - 7 x + 2

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Find the polynomial having roots at 2 and 31​ .

The polynomial generated from the given zeros is: P(x)=3x2−7x+2

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

The polynomial generated from the given zeros is: $P (x) = 3 x^{2} - 7 x + 2$