What is the solution of 3x^2 - 6x + 7 = 0

Expert Answers
justaguide eNotes educator| Certified Educator

The solution of a quadratic equation ax^2 + bx + c = 0 is `(-b+-sqrt(b^2 - 4ac))/(2a)`

For the equation 3x^2 - 6x + 7 = 0 the solution is `(6+-sqrt(36-84))/(6) = 1 +- (2/sqrt 3)*i`

The solution of the equation 3x^2 - 6x + 7 = 0 is `1 +- (2/sqrt 3)*i`

ericmilamattim | Student

There are three ways to answer quadratic equation

1. by factoring

2. completing the square

3. by quadratic formula

Since the given is not factorable and the leading coefficient is not 1 it is advisable to answer this using quadratic formula.

For any quadratic equation in the form of ax^2 + bx + c = 0

x=  `(-b+-sqrt(b^2 - 4ac))/(2a)`

so, for the equation  3x^2 - 6x + 7 = 0   the solution is 

 x= `(-(-6)+-sqrt((36) - 84))/6`

`x=1+-(2/sqrt(3))*i`

 

meaning there is no real solution only imaginary.

I hope this helps!

ericmilamattim | Student

There are three ways to answer quadratic equation

1. by factoring

2. completing the square

3. by quadratic formula

Since the given is not factorable and the leading coefficient is not 1 it is advisable to answer this using quadratic formula.

For any quadratic equation in the form of ax^2 + bx + c = 0

x=  

 

so, for the equation  3x^2 - 6x + 7 = 0   the solution is 

 

meaning there is no real solution only imaginary.

I hope this helps!