Question

Can someone check my answers for these three problems?
1. Use Descarte's Rule of Signs to describe the real zeroes of the function f(x)=2x^5-x^4-2x^3+4x^2+x-2.
a. The function has two or zero positive real zeroes and either three or one negative real zeroes.
b. The function has two or zero negative real zeroes and either three or one positive real zeroes.
c. The function has one positive real zeroes and either four or two negative real zeroes. (MY CHOICE)
d. The function has one negative real zeroes and either four or two positive real zeroes.

Answer 1

2. Use the Intermediate Value Theorem to choose an interval over which the function, f(x)=-2x^3-3x+5, is guaranteed to have a zero.
a. [-3,-2]
b. [-2,0]
c. [0,2]
d. [2,4]

3. Use the Rational Zero Theorem to select the values that are possible zeroes of the function f(x)=6x^3-2x^2+x+3. Select all that apply.
a. -3
b. -2/3
c. 3/2
d. 6

Answer 2

the equation is \[2x^{5} - x ^{4} - 2x ^{3} - 3x + 5\], correct?

Answer 3

No that is incorrect. @TGstudios I think that you accidentally mixed the equations from problems 1 and 2 together.

Answer 4

and\[f(x) = -2^{3} - 3x + 5\] and \[f(x) = 6x ^{3} - 2x ^{2} + x + 3\], correct?

Answer 5

yeah, the first one is\[2x ^{5} - x ^{4} - 2x ^{3} + 4x ^{2} + x - 2\], correct?

Answer 6

Both of those are correct @TGstudios

Answer 7

Yes, now the first one is correct as well @TGstudios

Answer 8

ok, sorry I don't know how to solve them, but those are to help others understand it