The graph below shows two polynomial functions, f(x) and g(x):

Mathematics

2 answers:

pentagon [3]2 years ago

5 0

One glance at the graphs should be enuf to tell you that one (the red one) is the graph of a parabola with positive leading coeff. and that the other is the gaph of an odd function which here happens to be y = x^3, also with a pos. lead. coeff.

neonofarm [45]2 years ago

3 0

The answer is '<span>f(x) is an odd degree polynomial with a positive leading coefficient'.

An odd degree polynomial with a positive leading coefficient will have the graph go towards negative infinity as x goes towards negative infinity, and go towards infinity as x goes towards infinity.

An even degree polynomial with a negative leading coefficient will have the graph go towards infinity as x goes toward negative infinity, and go towards negative infinity as x goes toward infinity.

g(x) would have a a positive leading coefficient with an even degree, as the graph goes towards infinity as x goes towards either negative or positive infinity.
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TiliK225 [7]

Answer:

$\frac{3x+4}{2x-2}$

Step-by-step explanation:

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8 0

2 years ago

Consider the equation 5x^2-10x+c=0. What values of c result in the equation having a complex solutions? Represent your answer on

stiv31 [10]

Answer:

When we have a quadratic equation:

a*x^2 + b*x + c = 0

There is something called the determinant, and this is:

D = b^2 - 4*a*c

If D < 0, then the we will have complex solutions.

In our case, we have

5*x^2 - 10*x + c = 0

Then the determinant is:

D = (-10)^2 - 4*5*c = 100 - 4*5*c

And we want this to be smaller than zero, then let's find the value of c such that the determinant is exactly zero:

D = 0 = 100 - 4*5*c

4*5*c = 100

20*c = 100

c = 100/20 = 5

As c is multiplicating the negative term in the equation, if c increases, then we will have that D < 0.

This means that c must be larger than 5 if we want to have complex solutions,

c > 5.

I can not represent this in your number line, but this would be represented with a white dot in the five, that extends infinitely to the right, something like the image below: