Solve
4y^4-4y^3+y^2=0

Question

Solve
4y^4-4y^3+y^2=0

zepdrix · Answer

$$\large 4y^4-4y^3+y^2=0$$Let's first factor out the LARGEST degree of y that each term contains.

It appears that they all contain at least y^2 right?
Which would give us,$$\large y^2\left(4y^2-4y+y^2\right)=0$$

zepdrix · Answer

Woops typo :O

zepdrix · Answer

$$\large y^2\left(4y^2-4y+1\right)=0$$

anonymous · Answer

y^2 ( 4y^2 - 4y +1) = 0

zepdrix · Answer

From there, we'll set each factor equal to 0 and solve for y.$$\large y^2=0 \qquad \qquad 4y^2-4y+1=0$$

zepdrix · Answer

That second part there, hmm. It's actually a perfect square, it might not be so easy to recognize though.

Throw it into the Quadratic Formula if you're having trouble with it.

Was any of that too confusing kitty? Pulling the y^2 out of each term maybe? :o

anonymous · Answer

I'll try the quadratic formula for that :)

anonymous · Answer

I got 1/2

zepdrix · Answer

Yah that sounds right for that one! c:

anonymous · Answer

Ooh thanks!

zepdrix · Answer

One tiny thing to keep in mind.
Our original equation was a 4th degree polynomial.
Meaning we'll end up with 4 roots (solutions for y).

We ended up with y=0 and y=1/2,
The reason we only have 2 answers is because they are both repeated roots.
y=0, y=0, y=1/2 and y=1/2 are technically all of the solutions.

Probably not something to worry about though ^^ yay good job!