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torisob [31]
2 years ago
12

Find the equation for a polynomial f(x) that satisfies the following:

Mathematics
1 answer:
denis-greek [22]2 years ago
3 0

Answer:

f(x) = 1/2(4 - x)(x - 1)(x - 2)

Step-by-step explanation:

Considering zero's and a coefficient, the function is:

f(x) = a(x - 4)(x - 1)(x - 2)

Considering y-intercept:

f(0) = a(0 - 4)(0 - 1)(0 - 2)

4 = a(-4)(-1)(-2)

4 = -8a

a = -1/2

So the function is:

f(x) = -1/2(x - 4)(x - 1)(x - 2) = 1/2(4 - x)(x - 1)(x - 2)

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Lilit [14]
Hello there!

The answer is C.

I will explain to you how I came to this answer.

•First of all, I counted the turning points. There are two, so that means this polynomial function has THREE roots. (# of turning points+1=number of roots.)

•Next, look to see how many times the function crosses the x-axis. This is the number of REAL solutions. In this case, there is one point at which the f(x) is crossing the x-axis so there is one real solution.

•Since there is one real solution there has to be 2 imaginary roots. (Total # of solutions-real solutions=imaginary solutions)

NOTE: the turning points are where the increasing intervals change to decreasing and the decreasing change to increasing. The first derivative at these points is 0.

I hope this helps!
Best wishes~
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3 years ago
Find the mean of 86, 87, 91, and 128
liraira [26]

Answer:

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Step-by-step explanation:

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Answer:

Take the root of both sides and solve.

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Step-by-step explanation:

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