Find the polynomial having roots at $2$ , $- \frac{1}{2}$ and $\frac{5}{3}$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 6 x^{3} - 19 x^{2} + 9 x + 10$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$2$	$x - 2$
$- \frac{1}{2}$	$2 x + 1$
$\frac{5}{3}$	$3 x - 5$

Step 2: Multiply the factors together:

P (x) = (x - 2) \cdot (2 x + 1) \cdot (3 x - 5) = 6 x^{3} - 19 x^{2} + 9 x + 10

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Find the polynomial having roots at 2 , −21​ and 35​ .

The polynomial generated from the given zeros is: P(x)=6x3−19x2+9x+10

Find the polynomial having roots at $2$ , $- \frac{1}{2}$ and $\frac{5}{3}$ .

The polynomial generated from the given zeros is: $P (x) = 6 x^{3} - 19 x^{2} + 9 x + 10$