Question
Factor the expression
v(v−2v2−1)
Evaluate
v2−2v3−v
Rewrite the expression
v×v−v×2v2−v
Solution
v(v−2v2−1)
Show Solution

Find the roots
v1=41−47i,v2=41+47i,v3=0
Alternative Form
v1≈0.25−0.661438i,v2≈0.25+0.661438i,v3=0
Evaluate
v2−2v3−v
To find the roots of the expression,set the expression equal to 0
v2−2v3−v=0
Factor the expression
v(v−2v2−1)=0
Separate the equation into 2 possible cases
v=0v−2v2−1=0
Solve the equation
More Steps

Evaluate
v−2v2−1=0
Rewrite in standard form
−2v2+v−1=0
Multiply both sides
2v2−v+1=0
Substitute a=2,b=−1 and c=1 into the quadratic formula v=2a−b±b2−4ac
v=2×21±(−1)2−4×2
Simplify the expression
v=41±(−1)2−4×2
Simplify the expression
More Steps

Evaluate
(−1)2−4×2
Evaluate the power
1−4×2
Multiply the numbers
1−8
Subtract the numbers
−7
v=41±−7
Simplify the radical expression
More Steps

Evaluate
−7
Evaluate the power
7×−1
Evaluate the power
7×i
v=41±7×i
Separate the equation into 2 possible cases
v=41+7×iv=41−7×i
Simplify the expression
v=41+47iv=41−7×i
Simplify the expression
v=41+47iv=41−47i
v=0v=41+47iv=41−47i
Solution
v1=41−47i,v2=41+47i,v3=0
Alternative Form
v1≈0.25−0.661438i,v2≈0.25+0.661438i,v3=0
Show Solution
