N&S Chapter 3: Quadratic problems

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Goal:

How to solve an(y) equation of the form

ax​2​​+bx+c=0

(or determine there are no solutions.)

a=0

ax​2​​+bx+c=0

That's a linear equation ...

b=0

ax​2​​+bx+c=0

Solve

x​2​​−9=0

Solve

x​2​​+9=0

2 solutions

1 solution

no solutions

c=0

ax​2​​+bx+c=0

Solve

x​2​​−9x=0

Solve

x​2​​+9x=0

a≠0∧b≠0∧c≠0

ax​2​​+bx+c=0

solve

x​2​​+6x−16=0

Can you solve the equation in one go?

Solve

(x+2)​2​​=9

Solve

(x+2)(2x−5)=0

Multiply out brackets

Don't multiply out brackets

Solving quadratic equations.

(If they don't have obvious solutions.)

Steps:

1. Multiply out brackets
   
   
2. Write in form 
   
   
3. Write in form
   
   
4. Determine which solution method you need 

ax​2​​+bx+c=0

x​2​​+​a​​b​​x+​a​​c​​=0

b=0

c=0

a,b,c =/= 0

Exercise

15, 17, 18