The index of ploynomial 1,0-3,0,5 taking x as variable?

x⁴ - 3x² + 5

Step-by-step explanation:

Given

Index = {1,0,-3,0,5}

Required

Represent as a polynomial

First, we need to get the degree (n) of the polynomial.

Because the given indices are 5,

Then

n = 5 - 1

n = 4

The polynomial is then represented as;

ax⁴ + bx³ + cx² + dx + e

Where

{a, b, c, d, e} = {1, 0, -3, 0, 5}

i.e.

a = 1 b = 0 c = -3 d = 0 e = 5

Substitute these values of a to e in the expression above:

ax⁴ + bx³ + cx² + dx + e

1x⁴ + 0x³ - 3x² + 0x + 5

x⁴ + 0 - 3x² + 0 + 5

x⁴ - 3x² + 5

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