- f(x) = 3x3 – 21×² – 54xZeroMultiplicityEffect

Mathematics

1 answer:

xenn [34]3 years ago

3 0

Answer:

x = 9 or x = 0 or x = -2

Step-by-step explanation:

Solve for x:

3 x^3 - 21 x^2 - 54 x = 0

The left hand side factors into a product with four terms:

3 x (x - 9) (x + 2) = 0

Divide both sides by 3:

x (x - 9) (x + 2) = 0

Split into three equations:

x - 9 = 0 or x = 0 or x + 2 = 0

Add 9 to both sides:

x = 9 or x = 0 or x + 2 = 0

Subtract 2 from both sides:

Answer: x = 9 or x = 0 or x = -2

You might be interested in

A farmer has both sheep and chickens on his farm. All the animals have the expected number of parts. When his animals are all

lora16 [44]

Answer:

13 sheep, 19 chicken

Step-by-step explanation:

You can start to solve this problem by assigning variables. First, let's assign the number of sheep there are as $x$ and the number of chickens there are as $y$ .

Because each sheep has 4 legs, the number of legs for each sheep would be $4x$ . Similarly, because each chicken has 2 legs, the number of legs for each chicken would be $2y$ . Each animal would have 1 head, so the number of heads would just be $x$ and $y$ . Because the number of legs in total are 90, $4x + 2y=90$ . Because the number of heads in total are 32, $x+y=32.$

There is now a system of equations with two unknown variables and two equations. There are many ways to solve this, but for me, the easiest would be elimination. First, I would double the second equation, $2x+2y=64$ . Then, I would subtract that from the first equation, eliminating $y$ . $2x=26$ . Solving for x gives 13. We can then plug that value into the second equation, making y be $32-13=19$ . This means that $x=13$ and $y=19$ , meaning that there are 13 sheep and 19 chicken.