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ElenaW [278]
3 years ago
13

Which correctly describes the roots of the following cubic equation? x3 – 5x² + 3x+9=0

Mathematics
1 answer:
Vikki [24]3 years ago
7 0

Answer:

-1 and 3

Step-by-step explanation:

First, note that there is an evident root in x=-1. You can see this because the coefficients of x3 and x sum the same number than the ones of x2 and the independent term (they sum 4: 1+3=4 and -5+9=4).

We can use this root to apply the Ruffini's rool with all the coefficients:

     1    -5    3   9

-1         -1     6  -9

     1    -6    9   0

This gives as that we can write the equation x3 – 5x² + 3x+9=0 as:

(x+1)*(x2-6x+9) = 0

The first term is due to the root x=-1 and the following is a product of Ruffini's rool. Now we need to find the 2 (at maximum) remaining roots, which are the roots of (x2-6x+9)=0

For this we could use Baskara's formula (you can try it) but lets do something simpler. We know that with the 2 roots, call them a and b, we can write the equation as: (x-a)(x-b)=0

If we apply distributive to (x-a)(x-b) we must get x2-6x+9. So, (-a)(-b) MUST be equal to 9. Working with integers there are not many options. Lets suppose a=b=3:

(x-3)*(x-3)=x2 -3x -3x + 9 = x2 - 6x + 9, and BINGO!

If we didnt get the results we could have tried with a=1 and b=9, for example, and so on. (please, compare with Baskara!).

So, we can write:

x3 – 5x² + 3x+9= (x+1)*(x-3)*(x-3) = (x-1)*(x-3)^2

And the roots are the values that make this equation zero:

x=-1 and x=3 where the last one is a double root.

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Amanda exercised for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40
anastassius [24]
The second one, Amanda's method is linear because the number of minutes increased by an equal number every week. Billy's method is linear because the number of minutes increased by an equal factor every week.
6 0
3 years ago
The value of y varies jointly with the values of x and z When x = 4 and z = 10, the value of y is 360.
Igoryamba

Answer:

A

Step-by-step explanation:

Joint variation is given by:

y=kxz

Where k is some constant.

We are given that y = 360 when x = 4 and z = 10. Therefore:

360=k(4)(10)

Solving for k:

40k=360\Rightarrow k=9

Therefore, our equation is:

y=9xz

Then when x = 5 and z = 12:

y=9(5)(12)=540

The answer is A.

3 0
3 years ago
Evaluate the function for the given value: f(x)=2x (to the power of 2) -5x-17, find f(-3)
lions [1.4K]

Answer:

f(-3) = 16

Step-by-step explanation:

You substitute -3 to x.

f(-3) = 2(-3)² - 5(-3) - 17

f(-3) = 16.

As for the coordinates, the coordinates plotted in the graph above are (1,-1) and (2,-2).

7 0
3 years ago
Read 2 more answers
Latesha buys some tennis balls at $1 each and rackets at $12 each for her PE class. She buys twice as many balls as rackets. She
marysya [2.9K]
I would go with A it makes most sense to me .
3 0
3 years ago
Find the value of z in the similar figures (round to the nearest tenth)
MrRa [10]
As they are similar figures,we can use the ratio of the side to find out the value of z.

The only side that both have the value indicated is 4 and 6,therefore we would use it to find the ratio.

The eqaution would be:
6/4 = z/8
3/2 = z/8
3×8 = 2z
z = 24/2
z = 12

Thus the value of z is 12.

Hope it helps!
4 0
3 years ago
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