Find the polynomial having roots at $0$ , $\frac{1}{2}$ and $- 3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 2 x^{3} + 5 x^{2} - 3 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$\frac{1}{2}$	$2 x - 1$
$- 3$	$x + 3$

Step 2: Multiply the factors together:

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

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Find the polynomial having roots at 0 , 21​ and −3 .

The polynomial generated from the given zeros is: P(x)=2x3+5x2−3x

Find the polynomial having roots at $0$ , $\frac{1}{2}$ and $- 3$ .

The polynomial generated from the given zeros is: $P (x) = 2 x^{3} + 5 x^{2} - 3 x$