Find the polynomial having roots at $\frac{2}{3}$ and $5$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 3 x^{2} - 17 x + 10$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$\frac{2}{3}$	$3 x - 2$
$5$	$x - 5$

Step 2: Multiply the factors together:

P (x) = (3 x - 2) \cdot (x - 5) = 3 x^{2} - 17 x + 10

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Find the polynomial having roots at 32​ and 5 .

The polynomial generated from the given zeros is: P(x)=3x2−17x+10

Find the polynomial having roots at $\frac{2}{3}$ and $5$ .

The polynomial generated from the given zeros is: $P (x) = 3 x^{2} - 17 x + 10$