What are the possible rational zeros of f(x) = 2x³ - 15x² + 9x + 22?

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) (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) = 2x³ - 15x² + 9x + 22

Here, constant term, p = +22

Leading coefficient, q = +2

The factors of the constant term +22 are ±1, ±2, ±11, ±22.

The factor of the leading coefficient is ±1, ±2.

Possible values of rational zeros p/q = ±1/±1, ±2/±1, ±11/±1, ±22/±1, ±1/±2, ±2/±2, ±11/±2, ±11/±2.

Therefore, the values of possible rational zeros are ±1, ±2, ±11, ±22, ±1/2, ±11/2.

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What are the possible rational zeros of f(x) = 2x³ - 15x² + 9x + 22?

Summary:

The possible rational zeros of f(x) = 2x³ - 15x² + 9x - 22 are ±1, ±2, ±11, ±22, ±1/2, ±11/2.