Question

State the possible rational zeros for each function.

Then find all rational zeros.
ƒ(x) = 3x³ + 22x² +28x - 35

Answer 1

no

Explanation:

The possible rational zeros of ƒ(x) = 3x³ + 22x² +28x - 35 are the factors of -35 divided by the factors of 3. These are:

-35/1 = -35, -35/-1 = 35

-35/3 = -5, -35/-3 = 5

Using the Rational Root Theorem, we can now test these values to see if they are zeros of the function:

-35: 3(-35)³ + 22(-35)² + 28(-35) - 35 = -8,925 + 30,950 + -980 - 35 = -9,880 which is not a zero

35: 3(35)³ + 22(35)² + 28(35) - 35 = 42,875 + 30,950 + 980 - 35 = 74,770 which is not a zero

-5: 3(-5)³ + 22(-5)² + 28(-5) - 35 = -125 + -100 + -140 - 35 = -400 which is not a zero

5: 3(5)³ + 22(5)² + 28(5) - 35 = 125 + 100 + 140 - 35 = 330 which is not a zero

So the function ƒ(x) = 3x³ + 22x² +28x - 35 has no rational zeros.

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