What are the possible rational zeros of f(x) = x⁴ + 2x³ - 3x² - 4x + 20?

Solution:

We can use the rational zero theorem to find rational zeros of a polynomial.

By Rational Zero Theorem,

If P(x) is a polynomial with integer coefficients and if is a zero of P(x) i.e.,(P( ) = 0),

then p is a factor of the constant term of P(x)

q is a factor of the leading coefficient of P(x)

Possible value of rational zero is p/q

Given, f(x) = x⁴ + 2x³ - 3x² - 4x + 20

Here, constant term, p = +20

Leading coefficient, q = +1

The factors of the constant term +20 are ±1, ±2, ±4, ±5, ±10, ±20.

The factor of the leading coefficient is ±1.

Possible values of rational zeros p/q = ±1/±1, ±2/±1, ±4/±1, ±5/±1, ±10/±1, ±20/±1

Therefore, the possible rational zeros are ±1, ±2, ±4, ±5, ±10, ±20.

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What are the possible rational zeros of f(x) = x⁴ + 2x³ - 3x² - 4x + 200?

Summary:

The possible rational zeros of f(x) = x⁴ + 2x³ - 3x² - 4x + 20 are ±1, ±2, ±4, ±5, ±10, ±20.