chapter 2-quadratic eqn_mdis

7/30/2019 Chapter 2-Quadratic Eqn_MDIS

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Quadratic Equation Page 1

Chapter 2 : Quadratic Equation

1. 02 cbxax is a quadratic equation.Must know Discussions

02

cbxax is a quadratic equationcbxaxy 2 is not a quadratic

equation but is a quadratic function. Each

quadratic function has a quadratic curve.

Find the solution of 0322 xx

Find the roots of 0322 xx

All these involve the finding of the values

ofx using one of these method :

1. By factorization2. By using formula3. Plot the graph of cbxaxy 2 Solve by using factorization. Example :Solve 0322 xx

If cannot factorize, solve by using formula :

a

acbbx

2

42

Example :Solve 032 xx

The roots of 02 cbxax are also the

x-intercepts of the quadratic curve of

cbxaxy 2 .

Solve by 02 cbxax by plotting the

graph of cbxaxy 2


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2. Nature of Roots in a quadratic equationMust know Discussions

Each quadratic equation can only have one of

these nature of roots ortype of roots :

Two roots aka real and distinct roots

No roor aka no real root One root aka real and equal root.

acbD 42 is known as discriminant. It

can be used to find the number of solutions or

roots for a quadratic equation.

real and distinct roots 042 acb

no real root 042 acb

real and equal root 042 acb

Find the nature of roots of the following :

032 xx

0122 xx

012 xx

How the root of quadratic equation related to

a quadratic curve ?

.

Real and distinct root related the quadratic

curve.

Real and equal root related the quadratic

curve.


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No real and root related the quadratic curve.


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3. Intersection between a straight line and a quadratic curve.

Nature of intersection

Examples

Equations :

kxmy

cbxxay 2

Nature of roots


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4. Basic Shaped of a quadratic curve : cbxaxy 2 :

Minimum Curve: Shaped Maximum Curve : Shaped Condition

Graph Shape

Convert

cbxaxy 2

to

khxay 2)(

by completing the

squares method

Examples

Sketch 6)5(2 2 xy Sketch 9)1( 2 xy

Sketch 2)2(2 xy Sketch 2)1(23 xy


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5. Completing the square : To convert cbxaxy 2 to khxay 2)(

Formula for completing the square Examples

cbxx 2 cbxx 2 22

22

bc

bx

Find the max/min values of the following :

(a) 32 xx

(b) xx 24 2

(c) xx 42

(d) 643 2 xx

(e) xx 3410 2


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6. Sketching quadratic curve cbxaxy 2

Steps to sketch graph Example

1. Find the y-intercept.:When x = 0, calculate y

2. Find the x-intercept.:When y = 0, find the roots

3. Determine turning points

4. Determine shape of graph( Shaped or Shaped )

5. Sketch the graph

Sketch the graph of 15246 2 xxy


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7. Solving Quadratic Inequalities.Steps to solve Example

1. Simplifed the given inequalities so thatthe R.H.S is zero, if necessary :

02 cbxax , 02 cbxax

02 cbxax , 02 cbxax

2. Find the roots of 02 cbxax usingfactorization or formula

3. Form the quadratic functioncbxaxy 2 and sketch a

simplifed quadratic curve with only

x-intercepts and eitherShaped

or Shaped

Solve 5222 xxx


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8. Sum and Product of roots.of 02 cbxax

Need to know Example

1. Suppose and are the roots of02 cbxax then

sum of rootsa

b

product of rootsa

c

2. Some useful identities :

Find the sum and product of roots of thefollowing :


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Example


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Example


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Worksheet :Quadratic Equation


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Answers :

9.

10. 01672 xx

11. (a) 0922 xx (b) 0453 2 xx

13. 33


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chapter 2-quadratic eqn_mdis

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