Quadratics

5 Discriminant, Problem Solving, Intersecting Graphs

The Discriminant (∆)

. roots real no are there0 If2

root real one is there0 If

2 and

2 roots real twoare there0 If

.4 is

0 quadratic a ofnt discrimina The2

2

ab

ab

ab

acbΔ

cbxax

Example 1 (Ex1E6)

09124 (c)

044 x(b)

0723 (a)

of roots theof nature thedetermine nt todiscrimina theUse

2

2

2

xx

x

xx

Example 2

roots.imaginary hasequation the(c)roots realdistinct twohasequation the(b)

root double a hasequation the(a):such that of values thefind Hence

nt.discrimina theformsimplest in find ,032For 2

kxkx

Problems

• Page 35 Exercise 1E6• Questions 1, 2, 3

Problem Solving with Quadratics

• Read question carefully.• Draw a diagram if appropriate to the question.• Use the information to write an equation.• Solve the equation• Examine the solutions to see if they are

appropriate to the problem.• Give your answer in a sentance.

Example 3

width.andlength its Find .cm 42 is area its and

widthitsn longer tha cm 3length has rectangleA 2

Example 4

tin.ofpiece original theof dimensions theFind .180cm volumeof

boxopen an form toup folded then are sidesresultant Thecorners. its ofout cut squares 5cm has tin of piece squareA

3

Example 5

?20cm area with triangleangledright a of legs

theform to wireoflength 12cm a bend topossibleit Is2

Problems

• Page 36 Exercise 1F• Questions 1, 2, 3, 4, 5, 6, 8, 9.

Intersecting Graphs

other.each toequal equations themake we x value thefind toHence on.intersecti of

point at the scoordinate same thehave graphs Two

xfy xgy

xgxf make isthat

Example 6

.82 and 132 graphs theofon intersecti of

points theof scoordinate themeans, algebraicby Find2 xyxxy

Problems

• Page 40 Exercise 1G• Questions 1, 2(a) (c) (e) (g).