Question

help please (: fan and medal

find the number of roots for each equation.

1. 2 - x^4 + x^2 = 0

explain pls <3

Answer 1

Step 1: Write the equation in standard form

Answer 2

most likely you can factor this , if it is a 'nice' book problem

Answer 3

it is order 4 from the x^4 term, it can have up to 4 solutions to that , zeroes, real or complex

Answer 4

Can you factor

x^2 - x - 2

?

Answer 5

(x-2)(x+1)

Answer 6

@DanJS

Answer 7

@DanJS @DanJS @DanJS

Answer 8

This equation can be re-written as: x^4 - x^2 +2 = 0
Plug y = x^2

Answer 9

good factoring, think of x^4 as [x^2]^2 and x^2 as [x]^2, lik telltoamit says, substitute u = x^2

u^2 - u + 2 = 0

you factored that to

(u - 2)(u + 1) = 0

now replace back the x^2 from the substitution u=x^2, and see what that does

Answer 10

(x^2 - 2) * (x^2 + 1) = 0

you can solve both those quantities and get 2 real and 2 complex roots

Answer 11

is tht the answer

Answer 12

no, remember solving these, if one quantity is zero, then the equation will be true, so you can solve

x^2 - 2 = 0
or
x^2 + 1 = 0

each of those will give you 2 answers

Answer 13

x^2 = 2
\[x = \pm \sqrt{2}\]

x^2 = -1

\[x = \pm \sqrt{-1} = \pm i\]

look good?

Answer 14

yea

Answer 15

most the time, if you have a higher order polynomial like that and they want you to solve it, most likely it will factor someway, if it is a book prob

Answer 16

is that the answer

Answer 17

it asks for the number of roots... roots means when the polynomial y=p(x) = 0 , is zero, when y=0, or the x-intercepts....

here you see it has 4 answers, in general, a polynomial of degree 'n' will have at most 'n' zeroes.

Answer 18

sorry, 'zeroes' and 'roots' mean the same

Answer 19

im soncused

Answer 20

here is a thing you can look over
http://cs.franklin.edu/~sieberth/MATH160/bookFiles/Chapter3/333371_0302_263-275.pdf