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The number of roots of any polynomial is given as the order of the polynomial. For n-order polynomial, the minimum number of roots are "n'. Given, f(x) = x^4 + 2x^3 – 3x^2 – 4x + 18, it has minimu of four roots. The given expression has the following roots ± 1, ± 2, ± 3, ± 6, ± 9, ± 18

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Answer:

The possible rational roots are ±1, ±2, ±3, ±6, ±9, ±18

Step-by-step explanation:

Given: \(f(x)=x^4+2x^3-3x^2-4x+18\)

We need to find all possible rational root of the given function.

Using rational root theorem test.

We have to factor the leading coefficient and constant term

Leading coefficient : 1

Constant term : 18

Factor of 18 (p): 1,2,3,6,9,18

Factor of 1 (q) : 1

We will divide each factor of 18 by each factor of 1.

Possible rational root: \(\pm\dfrac{p}{q}\)

Rational roots are:

\(\Rightarrow \pm1,\pm2,\pm3,\pm6,\pm9,\pm18\)

Hence, The possible rational roots are ±1, ±2, ±3, ±6, ±9, ±18

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