Loading....
Coupon Accepted Successfully!

 

Solved Examples

Example-1
Solve 3x2 + x - 2 = 0 for x.
Solution
Factor. (3x - 2)(x + 1) = 0
 
Use the principle of zero products, which says, if ab = 0, either a, b or both must be equal to zero.
3x - 2 = 0, x + 1 = 0
 
3x = 2, x = -1
 
x = (2/3)
 
x = -1, (2/3)
 
 
Example-2

Solve 3x2 + 5x = 0 for x.

Solution
Factor. x(3x + 5) = 0
 
Use the principle of zero products.
 
x = 0, 3x + 5 = 0
 
3x = -5
 
x = -(5/3)
 
x = 0, -(5/3)
 
 
Example-3
Solve 3x2 = 6 for x.
Solution
Recognize that the equation is quadratic because it is the same as 3x2 - 6 = 0.
 
Divide each side by 3.
 
x2 = 2
 
Take the square root of each side.
 
x =
 
 
Example-4

Solve 3x2 + 5x = -1 for x.

Solution
First find the standard form of the equation and determine a, b and c.
 
3x2 + 5x + 1 = 0
 
a = 3
 
b = 5
 
c = 1
 
Plug the values you found for a, b, and c into the quadratic formula.
 
Values of roots = 
 
Perform any indicated operations.


 
The solutions are as follows:
 

 
 
Example-5
Solve x4 - 9x2 + 8 = 0 for x.
Solution
Let u = x2. Then substitute u for every x2 in the equation.
 
u2 - 9u + 8 = 0
 
Factor.
(u - 8)(u - 1) = 0
 
Utilize the principle of zero products.
u - 8 = 0, u - 1 = 0
u = 8, u = 1
 
Now substitute x2 for u and solve the equations.
x2 = 8, x2 = 1
x = , x = ±1
x = ,
x = , ±1
 




Test Your Skills Now!
Take a Quiz now
Reviewer Name