Mathematics, 17.10.2019 14:50 treseanthegreat

What are the roots of the polynomial equation x4+x2=4x3-12x+12? use a graphing calculator and a system of equations. round no integer roots to the nearest hundredth
-12
–2.73, 2.73
–1.73, 1.73
12

Answers: 1

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Answers

Answer from: achoward08

I think the answer is c but i may be wrong, try using desmos online graphing calculator

Answer from: jacquetpaul1969

x = 2, x =-2, x = 1.73, x = -1.73

Step-by-step explanation:

We are given the equation:

$x^4+x^2=4x^3-12x+12\\x^4-4x^3+x^2+12x-12=0$

The attached image shows the graph for the given equation.

We can also factorize the given equation in the following manner.

By hit and trial method, we checked that 2 is a root of the given equation, that is,

(2)^4-4(2)^3+(2)^2+12(2)-12 = 0

Thus, we can write:

$(x-2)(x^3-2x^2-3x+6 ) = 0\\(x-2)(x^2(x-2)-3(x-2)) = 0\\(x-2)(x-2)(x^2-3) = 0\\(x-2)(x-2)(x-\sqrt3)(x+\sqrt3)=0\\x=2,x=-2, x = \sqrt3, x = -\sqrt3$

Thus, the roots of given equation are:

x = 2, x =-2, x = 1.73, x = -1.73

What are the roots of the polynomial equation x4+x2=4x3-12x+12? use a graphing calculator and a sys

Answer from: Quest

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

Answer from: Quest

Hello!

the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

$\frac{a^{m} }{a^{n} }=a^{m-n}$

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

$\frac{3^{4} }{3^{1}}$

then, calculating we have:

$\frac{3^{4} }{3^{1}}=3^{4-1}=3^{3}$

hence, the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

have a nice day!

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