Find the polynomial having roots at $4$ , $10$ and $1$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} - 15 x^{2} + 54 x - 40$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$4$	$x - 4$
$10$	$x - 10$
$1$	$x - 1$

Step 2: Multiply the factors together:

P (x) = (x - 4) \cdot (x - 10) \cdot (x - 1) = x^{3} - 15 x^{2} + 54 x - 40

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Find the polynomial having roots at 4 , 10 and 1 .

The polynomial generated from the given zeros is: P(x)=x3−15x2+54x−40

Find the polynomial having roots at $4$ , $10$ and $1$ .

The polynomial generated from the given zeros is: $P (x) = x^{3} - 15 x^{2} + 54 x - 40$