Question

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.

Answer 1

Explain to Felix that there are areas in the real world that involve number that are not real numbers ( do not exist on the real number line) These are referred to as "imaginary" numbers. There are also complex numbers that are part real and part unreal (imaginary). Electronics is an excellent example that involves both imaginary and complex. Then set Felix down and show him how to use the quadratic equation. When using the quadratic and run into taking the square root of a negative number, you have entered the world of the unreal! The square root of a -1 is referred to as "i" (imaginary number) in electronics it is referred to as the "j" operator, as i is used to represent current.

Answer 2

Alright so we need to create a discriminant of -1... and whenever we find the square root of -1 its "i"?

Answer 3

No, the problem says to create a discriminate that is negative, it could be a -1, but as long at it is negative.

Answer 4

alright I gotcha

Answer 5

any ideas?

Answer 6

Here is one that has a complex solutionL\[X ^{2}-8X+19=0\]Solve using quadratic equation.

Answer 7

can you walk me through solving it?

Answer 8

brb

Answer 9

back

Answer 10

when working with quadratics and discriminants, it's important to remeber the quadratic equation:

\[\frac {-b \pm \sqrt{b^2 - 4ac} }{2a}\]

the part under the square root is called the 'discriminanat'

if the discriminant is equal to -1, then
b^2 - 4ac = -1

so find some values for 'a', 'b' and 'c' so the equation is true.

once you have found those, replace the letters with the values you have into the quadratic form:
Y = ax^2 + bx + c