Question
Factor the expression
l3(1−l−l2)
Evaluate
l3−l4−l5
Rewrite the expression
l3−l3×l−l3×l2
Solution
l3(1−l−l2)
Show Solution

Find the roots
l1=−21+5,l2=0,l3=2−1+5
Alternative Form
l1≈−1.618034,l2=0,l3≈0.618034
Evaluate
l3−l4−l5
To find the roots of the expression,set the expression equal to 0
l3−l4−l5=0
Factor the expression
l3(1−l−l2)=0
Separate the equation into 2 possible cases
l3=01−l−l2=0
The only way a power can be 0 is when the base equals 0
l=01−l−l2=0
Solve the equation
More Steps

Evaluate
1−l−l2=0
Rewrite in standard form
−l2−l+1=0
Multiply both sides
l2+l−1=0
Substitute a=1,b=1 and c=−1 into the quadratic formula l=2a−b±b2−4ac
l=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
l=2−1±5
Separate the equation into 2 possible cases
l=2−1+5l=2−1−5
Use b−a=−ba=−ba to rewrite the fraction
l=2−1+5l=−21+5
l=0l=2−1+5l=−21+5
Solution
l1=−21+5,l2=0,l3=2−1+5
Alternative Form
l1≈−1.618034,l2=0,l3≈0.618034
Show Solution
