Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
a2(1−a−a2)
Evaluate
a2−a3−a4
Rewrite the expression
a2−a2×a−a2×a2
Solution
a2(1−a−a2)
Show Solution
Find the roots
a1=−21+5,a2=0,a3=2−1+5
Alternative Form
a1≈−1.618034,a2=0,a3≈0.618034
Evaluate
a2−a3−a4
To find the roots of the expression,set the expression equal to 0
a2−a3−a4=0
Factor the expression
a2(1−a−a2)=0
Separate the equation into 2 possible cases
a2=01−a−a2=0
The only way a power can be 0 is when the base equals 0
a=01−a−a2=0
Solve the equation
More Steps
Evaluate
1−a−a2=0
Rewrite in standard form
−a2−a+1=0
Multiply both sides
a2+a−1=0
Substitute a=1,b=1 and c=−1 into the quadratic formula a=2a−b±b2−4ac
a=2−1±12−4(−1)
Simplify the expression
More Steps
Evaluate
12−4(−1)
1 raised to any power equals to 1
1−4(−1)
Simplify
1−(−4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+4
Add the numbers
5
a=2−1±5
Separate the equation into 2 possible cases
a=2−1+5a=2−1−5
Use b−a=−ba=−ba to rewrite the fraction
a=2−1+5a=−21+5
a=0a=2−1+5a=−21+5
Solution
a1=−21+5,a2=0,a3=2−1+5
Alternative Form
a1≈−1.618034,a2=0,a3≈0.618034
Show Solution