## anonymous one year ago 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

1. mathstudent55

How do express a calm sentence in writing?

2. Vocaloid

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

3. Vocaloid

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

4. Vocaloid

|dw:1436918739549:dw|

5. anonymous

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

6. mathstudent55

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.

7. anonymous

Okay, Thank you.

8. Vocaloid

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