chapter 2-quadratic eqn_mdis
TRANSCRIPT
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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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14.