Find the polynomial having roots at $0$ , $\frac{1}{2}$ , $3$ and $- 4$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 2 x^{4} + x^{3} - 25 x^{2} + 12 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$\frac{1}{2}$	$2 x - 1$
$3$	$x - 3$
$- 4$	$x + 4$

Step 2: Multiply the factors together:

P (x) = x \cdot (2 x - 1) \cdot (x - 3) \cdot (x + 4) = 2 x^{4} + x^{3} - 25 x^{2} + 12 x

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Find the polynomial having roots at 0 , 21​ , 3 and −4 .

The polynomial generated from the given zeros is: P(x)=2x4+x3−25x2+12x

Find the polynomial having roots at $0$ , $\frac{1}{2}$ , $3$ and $- 4$ .

The polynomial generated from the given zeros is: $P (x) = 2 x^{4} + x^{3} - 25 x^{2} + 12 x$