How many solutions are there to this equation?

Question

3x^2 - 7x+12 =0

Thank You to all that answer! :)

Answer 1

wisestindianprophet is right.

Technically, there are 2, but your teacher will probably want the answer that there are 0.

That's because the 2 solutions are both "complex numbers".

This is because, as he says, the "discriminant" is zero.

The discriminant is the part underneath the square root symbol in the quadratic equation:

b² - 4ac

In your problem, that would be:

(-7)² - 4(3)(12) = 49 - 144 = -95

So if you were using the quadratic formula, you'd be taking the square root of -95.

Depending on what level of math you're in, either the answer is:

1) there are no real solutions, or
2) there are no real solutions (and two complex conjugate solutions).

Answer 2

Every simple quadratic has two, one or no real roots. To determine this, solve the determinete of the quadratic formula, (b^2 - 4ac)
7^2-4*3*12 = -95
Since it is negative, there are no real roots.
A zero would indicate one root.
Positive means two roots.

Answer 3

You need to use the quadratic formula:
x=-b±√b^2-4ac/2a
a=3,b=-7,c=12
x=-(-7)±√(-7)^2-4(3*12)/2(3)
x=7±√49-4(36)/6
x=7±√-95/6
There is no real solution.

Answer 4

Two. The highest power in your equation is equal to the number of solutions.

Answer 5

any proper equation will only have 1 solution which is the reason that math is referred to as an exact science

Answer 6

I think 2

Answer 7

They are nonreal solutions because the discriminant is <0.

If you still want them post again.

Answer 8

2 complex #'s