The graph of f(x) = x6 – 2×4 – 5×2 + 6 is shown below. How many roots of f(x) are rational numbers?

**Answer 1**

Two Rational Roots: 1 and -1 Walkthrough: See images for explanation!

**answer 2**

1,-1 are rational numbers Step-by-step explanation: Given equation: The roots of f(x) are: ⇒ ⇒ ⇒ ⇒ of these roots alone -1,1 is considered rational numbers because all integers are numbers rational. The others are irrational numbers.

**answer 3**

B.2

Step-by-step explanation: you answered the quiz correctly

**answer 4**

B Walkthrough: the roots would be 1 and -1 with respect to the graph

**Answer 5**

There are two rational roots for f(x) Walkthrough: We are given a function to find the number of rational roots for f(x). Let’s use the remainder theorem that when f(a) = 0, (xa) is a factor of f(x) or x=a is a solution. Replace 1 by xf(1) = 1-2-5+6=0 So x=1 is a solution. Let’s try x=-1 f(-1) = 1-2-5+6 =0 So x =-1 is also a solution and x+1 is a factor We can write f(x) by trial and error as We find that the factor gives two irrational solutions as ±√3. The number of rational roots is therefore 2.

**Answer 6**

STEP 6 Walkthrough: Another guy is WONRG on the edge

**Answer 7**

B.2 Step-by-step explanation: e.g. 2021

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