NEED HELP ASAP ILL GIVE 30 POINTS
1 answer:
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There is a multiple zero at 0 (which means that it touches there), and there are single zeros at -2 and 2 (which means that they cross). There is also 2 imaginary zeros at i and -i.
You can find this by factoring. Start by pulling out the greatest common factor, which in this case is -x^2.
-x^6 + 3x^4 + 4x^2
-x^2(x^4 - 3x^2 - 4)
Now we can factor the inside of the parenthesis. You do this by finding factors of the last number that add up to the middle number.
-x^2(x^4 - 3x^2 - 4)
-x^2(x^2 - 4)(x^2 + 1)
Now we can use the factors of two perfect squares rule to factor the middle parenthesis.
-x^2(x^2 - 4)(x^2 + 1)
-x^2(x - 2)(x + 2)(x^2 + 1)
We would also want to split the term in the front.
-x^2(x - 2)(x + 2)(x^2 + 1)
(x)(-x)(x - 2)(x + 2)(x^2 + 1)
Now we would set each portion equal to 0 and solve.
First root
x = 0 ---> no work needed
Second root
-x = 0 ---> divide by -1
x = 0
Third root
x - 2 = 0
x = 2
Forth root
x + 2 = 0
x = -2
Fifth and Sixth roots
x^2 + 1 = 0
x^2 = -1
x = +/-
x = +/- i
Answer:
a) Table and graph showed
b) The distance will be 231 miles
c) Yes
Step-by-step explanation:
We know the van gets 22 mi/gal, so the distance D in miles traveled by the van can be expressed as
D(g)=22g, being g the number of gallons of gas used
a) The graph of the function D and its corresponding table of values is shown below.
b) If the van used g=10.5 gallons of gas, the distance would be:
D(10.5)=22 x 10.5 = 231 miles
c) The values of g are real in nature because they represent the amount of gas consumed by the van and it can be any real positive number. Being D a linear function of g, it also happens to take positive real values. Then it makes sense to connect the points with lines.
