Find the polynomial having roots at $1$ , $\frac{1}{4}$ , $\frac{1}{9}$ and $\frac{1}{16}$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 576 x^{4} - 820 x^{3} + 273 x^{2} - 30 x + 1$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$1$	$x - 1$
$\frac{1}{4}$	$4 x - 1$
$\frac{1}{9}$	$9 x - 1$
$\frac{1}{16}$	$16 x - 1$

Step 2: Multiply the factors together:

P (x) = (x - 1) \cdot (4 x - 1) \cdot (9 x - 1) \cdot (16 x - 1) = 576 x^{4} - 820 x^{3} + 273 x^{2} - 30 x + 1

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Find the polynomial having roots at 1 , 41​ , 91​ and 161​ .

The polynomial generated from the given zeros is: P(x)=576x4−820x3+273x2−30x+1

Find the polynomial having roots at $1$ , $\frac{1}{4}$ , $\frac{1}{9}$ and $\frac{1}{16}$ .

The polynomial generated from the given zeros is: $P (x) = 576 x^{4} - 820 x^{3} + 273 x^{2} - 30 x + 1$