Question

Medal will be given,
Roy exclaims that his quadratic with a discriminant of –9 has no real solutions. Roy then puts down his pencil and refuses to do any more work. Create an equation with a negative discriminant. Then explain to Roy, in calm and complete sentences, how to find the solutions, even though they are not real

Answer 1

How do express a calm sentence in writing?

Answer 2

general form of a quadratic equation is

ax^2 + bx + c
and the discriminant is

square root(b^2-4ac)

you can pick three values of a, b, and c such that square root(b^2-4ac) is positive

Answer 3

we can still use the quadratic formula to find the solutions, like we would with real solutions, but we'll need to evaluate the nonreal discriminant

Answer 4

actually Roy is correct btw

surely, there are "imaginary" solutions
but Roy said there were no "real" ones, and he's correct

Answer 5

Here is the quadratic formula:

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

It is the solution to a quadratic equation of the form:

\(ax^2 + bx + c = 0\)

Notice that the quadratic formula contains the part \(b^2 - 4ac\) inside the root. If you pick numbers for a and c that when multiplied together and subtracted from \(b^2\) will result in a negative number, a negative discriminant, then the solutions to the quadratic equation will definitely be complex.

Answer 6

Okay, Thank you.

Answer 7

yeah, listen to mathstudent's answer, it's better than mine