Question

PLEASE HELP! Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

5, -3, and -1 + 3i

Answer 1

Given zeros: 5, -3, and -1 + 3i, -1 - 3i has to be another zero since complex zeros come in pairs and -1 - 3i is the complex conjugate of -1 + 3i. You get the polynomial:

f(x) = (x - 5)(x + 3)(x - (-1 + 3i))(x - (-1 - 3i))

f(x) = (x² - 2x - 15)(x² + 2x + 10)

f(x) = x⁴ + 2x³ + 10x² - 2x³ - 4x² - 20x - 15x² - 30x - 150

f(x) = x⁴ - 9x² - 50x - 150

Answer 2

could you help me with another question please @Lunalovegood

Answer 3

sure :)

Answer 4

What's your question?

Answer 5

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x)= x-8/x+7 g(x)= -7x-8/x-1

Answer 6

(g(x)) = [(-7x-8)/(x-1) - 8} / [(-7x - 8)/(x-1) + 7] =

[(-7x - 8 - 8(x-1)) / (x-1)] / [(-7x - 8 + 7(x-1)) / (x-1)] = (-15x) / (-15) = x.

g(f(x)) = [-7*(x-8)/(x+7) - 8] / [(x-8)/(x+7) - 1] =

[(-7x + 56 -8*(x+7)) / (x+7)] / [(x - 8 - (x + 7)) / (x+7)] = (-15x) / (-15) = x.

So since f(g(x)) = g(f(x)) = x we can conclude that f and g are inverses.

Answer 7

Thank you!! i have 2 more and thats it! 1st Identify intervals on which the function is increasing, decreasing, or constant.

g(x) = 1 - (x - 6)2

Answer 8

hmm... I'm not quite sure about this one. I can probably help you with your other question, and then get someone to help you with this one

Answer 9

Find the inverse of the function.

f(x) = the cube root of x divided by eight. - 4

Answer 10

Umm.. I'll get someone to help you with these to questions, sorry I could not help you with these.

Answer 11

@AccessDenied could you help @Eleanor12 with her questions?

Answer 12

THANK YOU SO MUCH!!! @Lunalovegood

Answer 13

No Problem