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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Which exponential functions have been simplified correctly check all that apply

Fittoniya [83]

Principle: Law of Exponents - Combination of product to a power & power to a power. The first is when raising a product of two integers to a power, the power is distributed to each factor. In equation it is,

(xy)^a = (x^a)(y^a)

The latter is when raising the base with a power to a power, the base will remain the same and the powers will be multiplied. In equation it is,
(x^a)(x^b) = x^ab

Check:

f(x) = 5*(16)^.33x = 5*(8*2)^0.33x = 5*(8^0.33x)(2^0.33x) = 5*(2^x)*(2^0.33x) = 5*(2^1.33x)

f(x) = 2.3*(8^0.5x) = 2.3*(4*2)^0.5x = 2.3*(2^x)(2^0.5x) = 2.3*(2^1.5x)

f(x) = 81^0.25x = 3^x

f(x) = 0.75*(9*3)^0.5x = 0.75*(3^x)*(3^0.5x) = 0.75*3^1.5x

f(x) = 24^0.33x = (8*3)^0.33x = (2^x)*(3^0.33x)

Therefore, the answer is third equation.

<em>ANSWER: f(x) = 81^0.25x = 3^x</em>

5 0

3 years ago

Read 2 more answers

An animal shelter has $2500 in its reserve fund. The shelter charges $40 per animal placement and would like to have at least $4

densk [106]

Answer:

Step 1

Write and solve the inequality:

2,500 + 40a ≥ 4,000, or 40a ≥ 1,500

a ≥ 37.5

Step 2

If the shelter places 30 cats and 10 dogs,