Consider the polynomial p(x)=x⁴-3x²-4.what are the solutions to x⁴-3x²-4=0.

The solutions are and .

Step-by-step explanation:

We have the following equation:

.

The first step to solve this problem is using

We replace in the equation 1, find the values of y, and then we replace in equation 2) to find the values of x.

To solve the equations, it is important to know how we find the roots of a second order polynomial.

Given a second order polynomial expressed by the following equation:

This polynomial has roots such that , given by the following formulas:

In this problem, we have

So

So:

The values of y are

We also have that:

So

And

There is no real solution for this. So our only solutions are and .

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}