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Thepotemich [5.8K]
3 years ago
14

What are the roots of the polynomial equation x4+x2=4x3-12x+12? use a graphing calculator and a system of equations. round no in

teger roots to the nearest hundredth
-12
–2.73, 2.73
–1.73, 1.73
12

Mathematics
2 answers:
Romashka [77]3 years ago
7 0
I think the answer is c but i may be wrong, try using desmos online graphing calculator
Mumz [18]3 years ago
6 0

Answer:

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

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Step-by-step explanation:

To find the prime factorization of a number, start by dividing the number by each prime number that you can divide by as many times as possible, starting with the smallest prime number and moving up. Then move on to the next prime number. The last division must give a quotient of 1. Then the prime factorization is the product of all the prime factors you divided the number by.

Here's how you use this method with 180.

Here are the first 10 prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Start by trying to divide by 2. 180 is divisible by 2.

180/2 = 90       90 is divisible by 2.

90/2 = 45         45 is not divisible by 2, so now try 3.

45/3 = 15          15 is divisible by 3.

15/3 = 5            5 is prime, so it is divisible by 5.

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Answer: 5

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