Question

Find all of the zeros of the equations below. Show all of your work.
1) x3 – 5x2 + 6x = 0
2) x4 – 8x2 – 9 = 0
3) 5x3 – 5x = 0
This is the only thing I have left to do and I have no idea how to do it, please help

Answer 1

1.\[x \left( x^2-5x+6 \right)=0,either~ x=0,or~x ^{2}-3x-2x+6=0,make factors\]

Answer 2

Can you factor these equations?

Answer 3

if you factor them you get:
for number one you get:
\[x(x^2-5x+6)=0\]
using the zero factor property you know that either x = 0
or \[x^2-5x+6=0\]
so so far we know that 0 is a solution
now solve the quadratic:
\[(x-3)(x-2)=0\]
x=3 or x=2

So the zeroes for the first equation are 0,2, and 3

Answer 4

\[x^4-8x^2-9=0\]
\[put ~x^2=y,x^4=y^2\]
\[y^2-8y-9=0\]
1*-9=-9
9-1=8
9*-1=-9
-8y=-(9-1)y=-9y+1y
\[y^2-9y+1y-9=0,y \left( y-9) \right)+1\left( y-9 \right)=0\]
\[\left( y-9 \right)\left( y+1 \right)=0\]
either y-9=0,y=9
\[x ^{2}=9,x=\pm 3\]
or y+1=0,y=-1
\[or~x ^{2}=\iota ^{2},x=\pm \iota \]

Answer 5

3.
\[5x ^{3}-5x=0,5x \left( x ^{2}-1 \right)=0,5x \left( x+1 \right)\left( x-1 \right)=0\]
Hence x=0,-1,1