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3 years ago

What are the possible numbers of positive, negative, and complex zeros of f(x) = 3x4 − 5x3 − x2 − 8x + 4?

Mathematics

1 answer:

Scorpion4ik [409]3 years ago

3 0

Answer:

Two positive zeros, no negative zeros, two complex roots.

Step-by-step explanation:

The given function is $f(x)=3x^4-5x^3-x^2-8x+4$

According to the fundamental theorem of algebra, the function will have 4 roots.

The graph of the function intersects the positive axis at two points.

Hence the function has two positive zeros and no negative zeros.

The two remaining roots are imaginary. The function has two complex zeros.

See graph in attachment

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Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3. (5 points)

OLEGan [10]

Answer:

From given option , the equation of parabola is y = negative x² divided by 12

Step-by-step explanation:

Given as for parabola :

The focus is at (0 , - 3)

The directrix equation is y = 3

Now, equation of parabola parallel to y-axis is

( x - h )² = 4 p ( y - k )

where focus is ( h , k+p ) and directrix equation is y = k - p

So, from equation

h = 0 and k + p = - 3

And y = k - p i.e k - p = 3

Now solving ( k + p ) + ( k - p ) = - 3 + 3

or, 2 k = 0 ∴ k = 0

Put the value of k , k + p = - 3

So, 0 + p = - 3 ∴ p = - 3

Now equation of parabola with h = 0 , k = 0 , p = - 3

( x - h )² = 4 p ( y - k )

I.e ( x - 0 )² = 4 × ( - 3 ) ( y - 0 )

Or, x² = - 12 y is the equation of parabola

Hence From given option , the equation of parabola is y = negative x² divided by 12 Answer

7 0

3 years ago

Please help! 15 Points! How do i do this? (View the picture down below)

Nadya [2.5K]

Ok, so what this question is really asking you is: $2/5=0.4$

What is $6*0.4$ and that equals $6*0.4=2.4$

Now because the the number is 2.4 plot that point

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3 years ago

Meg wants to take tennis lessons. In the chart, four instructors are listed with what they charge. Which instructor gives the be

Ierofanga [76]

So,

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Finally, Andy wants $60 for 5 hrs., or $12/hr.

We can see that <u>Rick</u> offers the best deal, at $8.89/hr.

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3 years ago

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A bag contains an orange tile, a yellow tile, and a purple tile. Two tiles are drawn randomly without replacement. If the first

Tcecarenko [31]

Answer:

1 out of 2

Step-by-step explanation:

You already took out on tile from the bag, yellow. Now you are left with 2, meaning that it is a 50/50 chance of you pulling out the orange tile

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3 years ago

Which statement best compares the graphs of y=-3x^n and y=3x^n?

devlian [24]

Answer:

The graph of y=-3x^n is the reflection of the graph of y=3x^n about the x axis.

Step-by-step explanation:

If you graph these two functions, then you will notice that they look similar. for example the points of (1,-3) on graph y=-3x^n and point (-1,-3) on graph y=3x^n. They have the same y value but just the reflection of the x value. I hope this helped !!

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4 years ago

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