Quadratics

Solving Quadratic Equations

Solving by Factorising

equations. elementary theSolve :3 Step

.0or 0either

then,0 if :lawfactor null the Use:3 Step

side.other thefactoriseFully :2 Step

side. one to termsall ingby tranfer

zero toequalequation theof side one make :1 Step

rue.equation t themake which of valuesare

0cbx of solutionsor Roots:Definition 2

ba

ba

x

ax

Example 1

72

3 (e)

10116 (d)

414 (c)

65 (b)

053 (a)

:for x following theSolve

2

2

2

2

xx

xx

xx

xx

xx

Solving by Completing the Square

for x. valuesthe

find andequation theundo toable then are We

square. the

completing of method theusingby

form in the 0 writeWe2

2

qpxa

cbxax

Example 2

073 (c)

75 (b)

3232 (a)

:for x Solve

2

2

2

x

x

x

Example 3

03102 (c)

043 (b)

014 (a)

:square thecompletingby following theSolve

2

2

2

xx

xx

xx

Solving using the Quadratic Formula

a

acbbx

cbxax

2

4

:is 0 osolution t The

2

2

Proof

Example 4

133-x

5x (d)

0432 (c)

022 (b)

0103 (a)

:formula quadratic theusing following theSolve

2

2

2

x

xx

xx

xx

Approximate solution using Technology

• Draw the graph using the graphic calculator In y=

• Use an appropriate window• Find where the graph cuts the x-axis using 2nd

calc buttons

Example 5

1221x (c)

0143x (b)

0115 (a)

:osolution t eapproximat thefind y to technologUse

2

2

xx

x

xx

Complex Roots

• Use the quadratic formula to solve• If the number under the square root is

negative treat it as an imaginary number and continu with the solution.

Example 6

0134 (c)

0254x (b)

09 (a)

:for x Solve

2

2

2

xx

x

This Weeks Work

• Page 26 Ex 1E1 Q1 – 3• Page 28 Ex1E2 Q1 – 3• Page 31 Ex 1E3 Q1, 2• Page 12 Ex 1E4 Q1, 2• Page 33 Ex 1E5 Q1, 2