Need help with Quadratics and Discriminant. Thank you!!

Question

1. You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.

1. a. graphing
2. b. factoring
3. c. square root method
4. d. completing the square
5. e. quadratic formula

2. What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?

Answer 1

Graphing is useful for checking your answer, if the math got a little tedious such that mistakes are easy to make

factoring requires trial and error and generally only works if you have simple numbers such as

x^2 -3x +4 '

(x-4)(x+1)=0

x=-1, 4

square root is if you only have a quadratic term

x^2 = 64

x = + or - sqr64 = + or - 8

completing the square is good when the x^2 term has 1 for the coefficient

and the x term is even.

x^2 +4x + 4

If you don't notice you can factor it, do completing the square

x^2 + 4x = -4

then add half the coefficient of the x term squared. half of 4 is 2, square it to get 4

then add 4 to both sides

x^2 +4x + 4 = -4 + 4

then you have a perfect square on the left side

(x+2)^2 = 0

x = -2

There's technically 2 solutions, but they're identical, both -2

quadratic formula is used when nothing else looks promising

6x^2 + 7x -19 =0

x= [-b + or - sqr(b^2 - 4ac)]/2a

where b=7, a=6 and c=-19

so

x= [-7+ or - sqr(49+4(6)(9)]/2