Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
z2(z−1)(z+1)
Evaluate
z4−z2
Factor out z2 from the expression
z2(z2−1)
Solution
More Steps
Evaluate
z2−1
Rewrite the expression in exponential form
z2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(z−1)(z+1)
z2(z−1)(z+1)
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Find the roots
z1=−1,z2=0,z3=1
Evaluate
z4−z2
To find the roots of the expression,set the expression equal to 0
z4−z2=0
Factor the expression
z2(z2−1)=0
Separate the equation into 2 possible cases
z2=0z2−1=0
The only way a power can be 0 is when the base equals 0
z=0z2−1=0
Solve the equation
More Steps
Evaluate
z2−1=0
Move the constant to the right-hand side and change its sign
z2=0+1
Removing 0 doesn't change the value,so remove it from the expression
z2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
z=±1
Simplify the expression
z=±1
Separate the equation into 2 possible cases
z=1z=−1
z=0z=1z=−1
Solution
z1=−1,z2=0,z3=1
Show Solution