Find the polynomial having roots at $0$ , $3$ , $\frac{9}{2}$ and $10$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 2 x^{4} - 35 x^{3} + 177 x^{2} - 270 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$3$	$x - 3$
$\frac{9}{2}$	$2 x - 9$
$10$	$x - 10$

Step 2: Multiply the factors together:

P (x) = x \cdot (x - 3) \cdot (2 x - 9) \cdot (x - 10) = 2 x^{4} - 35 x^{3} + 177 x^{2} - 270 x

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Find the polynomial having roots at 0 , 3 , 29​ and 10 .

The polynomial generated from the given zeros is: P(x)=2x4−35x3+177x2−270x

Find the polynomial having roots at $0$ , $3$ , $\frac{9}{2}$ and $10$ .

The polynomial generated from the given zeros is: $P (x) = 2 x^{4} - 35 x^{3} + 177 x^{2} - 270 x$