Question

AWARDING MEDALS!

Justify if completing the square is a good method for solving when the Discriminant is negative. Use any of your three functions as an example and respond in complete sentences.

Answer 1

F(x) = (x-1) (x-2)

Answer 2

please?

Answer 3

well completing the square will give you the answer in the same for as the general quadratic formula

as an example consider

\[x^2 +2x + 4 = 0\]

the discriminant is

\[\Delta = -12\]

so using the general quadratic formula the solutions are

\[x = \frac{-4 \pm \sqrt{2^2 - 4 \times 1 \times 4}}{2 \times 1}\]

which simplifies to

\[x = -1 \pm \sqrt{-3}...or ... x = -1 \pm i \sqrt{3}\]

now if you rewrite the problem

\[x^2 +2x = -4\]

add halve the coefficient of the middle termed squared to both sides of the equation

\[(\frac{2}{2})^2 = 1\]

so you have

\[x^2 + 2x + 1 = -3\]

which is

\[(x + 1)^2 = -3\]

I'll let you finish to show that the solution is the same as using the general quadratic formula

Answer 4

okay thank you!!