What is the discriminant of the quadratic equation 3 – 4x = –6x2?

The discriminant is the stuff under the square root in the quadratic equation. Let's first get this equation in standard form. This must equal 0! Let's see what we have:

Since we need this quadratic to equal 0 to use the quadratic formula, add to both sides.

Note that I just rearranged the -4 and +3 to make it in the form. Now, let's put this in the quadratic equation.

Since we are only solving for the discriminant, let's simplify the expression under the square root.

Now, since we have a negative number in the discriminant, we know that neither of the solutions will be real numbers. They will be in terms of ()

The simplified version of the discriminant is:

However, if you have not learned imaginary numbers yet, you can say the discriminant is -56.

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: