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

Answer

The polynomial generated from the given zeros is: $P (x) = 15 x^{3} - 23 x^{2} + 9 x - 1$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (5 x - 1) \cdot (3 x - 1) \cdot (x - 1) = 15 x^{3} - 23 x^{2} + 9 x - 1

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Find the polynomial having roots at 51​ , 31​ and 1 .

The polynomial generated from the given zeros is: P(x)=15x3−23x2+9x−1

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

The polynomial generated from the given zeros is: $P (x) = 15 x^{3} - 23 x^{2} + 9 x - 1$