Felix exclaims that his quadratic with a discriminant of −1 has no real solutions. Felix then puts down his pencil and refuses to do any more work. Create an equation with a negative discriminant. Then explain to Felix, in calm and complete sentences, how to find the solutions, even though they are not real.

Question

anonymous · Answer

@phi

phi · Answer

Have you created an equation with a negative discriminant ?
i.e. where
b^2 -4ac is < 0

anonymous · Answer

nope :l

anonymous · Answer

so 1^2 - 4(2)(3)?

anonymous · Answer

b = 1
a = 2
and c = 3?

phi · Answer

now write down that quadratic , and set = to zero

anonymous · Answer

how do I write it as a quadratic?

phi · Answer

the a,b and c are the coefficients of x^2, x and x^0

anonymous · Answer

ax^2 + bx + c is the quadratic formula right?

anonymous · Answer

b = 1 a = 2 and c = 3

2x^2 + 1x + 3

phi · Answer

no, that is the standard form of a quadratic

the quadratic formula is how you solve it.


***
now write down that quadratic , and set = to zero
***

anonymous · Answer

so what?
2x^2 + 1x + 3 = 0 would be it?

phi · Answer

it is understood that the "solutions" are what x values make the quadratic = 0

now that you have
$$ 2x^2 + x + 3 = 0 $$
(people don't bother to write a 1 as a coefficient... no number means 1)
you solve it
You could use "complete the square" to solve it.

anonymous · Answer

what do we do first in the complete the square method?

phi · Answer

Go get some popcorn, and watch this http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_formula_tutorial/v/solving-quadratic-equations-by-completing-the-square

anonymous · Answer

ahh 14min lol

phi · Answer

It is a great video...especially if you have popcorn with it.

anonymous · Answer

ok I got past the part where he completed the square

anonymous · Answer

$$2x^2 + 1x + 3 = 0$$
we already have 3 terms on the left side though o_O

anonymous · Answer

you there @phi?

phi · Answer

If you got far enough, you should divide both sides by 2 (to get a coefficient of 1 in front of x^2)

anonymous · Answer

so 1x^2 + 1x + 3 = 0

anonymous · Answer

or just x^2 + 1x + 3 = 0

phi · Answer

divide *everything* by 2

anonymous · Answer

ok
x^2 + 1/2x + 3/2 = 0

phi · Answer

now try to finish it.

anonymous · Answer

x^2 + 2x = 0
-2x
x^2 = -2?

phi · Answer

start with 
x^2 + 1/2x + 3/2 = 0

now review the video.

anonymous · Answer

we square 1/2 and 3/2?

anonymous · Answer

which is 1/4 and 9/4?