Question

find all square roots.
4 answers
x^4 - 8x^3 + 25x^2 = 0

Answer 1

just factor it

Answer 2

i tried

Answer 3

ok what is your first step?

Answer 4

all terms have an x,
that means you can __________?

Answer 5

factor out?

Answer 6

can u use the quadratic formula in this equation

Answer 7

not yet

Answer 8

just answer my questions

Answer 9

what is your first step?
all terms have an x, that means you can factor out __________?

Answer 10

the x^2

Answer 11

ok so once you factor that out, what does the equation look like?

Answer 12

x^2 ( x^2 - 8x + 25)

Answer 13

= 0

Answer 14

ok now remember the zero property of multiplication
anythign multiplied by zero is equal to zero

this means either x^2 is equal to zero
or x^2-8x+25 is equal to zero


now lets start by looking at x^2=0

what are the 2 roots (well one root)
x=?

Answer 15

in other words
x^2 =0

x =?

Answer 16

...
1^2= 1
1 is not equal to zero.....

Answer 17

0?

Answer 18

yes...

Answer 19

2 of your roots would be zero

x^2 = x *x =0

recalling zero property of multiplication
x=0 and x=0

Answer 20

do you understand this?

Answer 21

yea so far.

Answer 22

good, so we know two of the roots, now to find the other two

recalling zero property of multiplication
x^2-8x+25 must also be equal to zero

x^2-8x+25=0
we need to factor this in order to determine the 2 roots

unfortunately, if you try, you will realize that you cannot not factor it with normal means

this is where the quadratic equation comes in

Answer 23

in otherwords

use the quadratic equation to determine hte other 2 roots

Answer 24

okay thanks