Solving Quadratics and the Discriminant Assignment

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

2)

For quadratic equaton ax^2+bx+c=0, The discriminant is b^2-4ac.

If the discriminant is zero, then the equation has only one solution,

namely -b/(2a)

if the discriminant is a positive perfect square, then the

equation as TWO RATIONAL SOLUTIONS. In THIS CASE, the equation

can be factored

if the discriminant is a positive NON-perfect square, then

the equationhas TWO REAL (but irrational) solutions

containing radicals

if the disciminant is NEGATIVE, ask you have asked,

then the equation has TWO imaginary/complex solutions

#1)

(b)

x^2 + 5x+ 6 = 0 is best solved by factoring (x + 3)(x+2 ) = 0

is easy to factor. Always check if it can be factored.

(c) x^2 = 81 is best solved by square root method as the

calculation of the square root is easy. If A=1 C is a negative

perfect square , then the square root method is easy.

(d) x^2 + 4x = 11 is best solved by completing the square because

B is an even integer. If A=1 and B is an even number, then it

is easy to complete the square

(e) otherwise you use the quadratic formula