Form 4 Add Math Chapter 2

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  • Topic: Quadratic equation, Completing the square, Elementary algebra
  • Pages : 2 (256 words )
  • Download(s) : 282
  • Published : February 15, 2013
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2.2 Solving Quadratic Equation
A quadratic equation can be solved by using:
1. Factorization
i) Arrange the unknowns in general form (ax2+bx+c=0) and factorize it 2. Completing the square
i) x2-6x+4=0
ii) x2-6x=-4
iii) x2-6x+-622=-4+-622
iv) x2-6x+-32=-4+-32
v) x-32=5
vi) x-3=±5
vii) x=3±5
viii) x=3+5 OR 3-5
ix) x=5.236/0.7369

3. Quadratic formula
x=-b±b2-4ac2a
* Forming quadratic equation from given roots
SOR=sum of roots POR=product of roots
SOR=-ba POR=ca
.x2-α+βx+αβ=0
.x2-SORx+POR=0
* Types of roots
b2-4ac>0| Two different roots| Straight line intersects a curve at two different points| b2-4ac=0| Two equal roots| Straight line touches the curve at one point/ tangent to the curve| b2-4ac<0| No real roots| Straight line does not intersect the curve|

Example Questions:
1. Show that the quadratic equation x2=21-kx-9-k2 has two real roots for k≤-4. Solution:
.x2-21-kx+9+k2=0
.a=1, b=-2+2k, c=9+k2
Since it has 2 real roots,
.b2-4ac≥0 {It didn’t mention that the 2 roots are equal roots or different roots, so it can be >0/=0 that becomes ≥0} .(-2+2k)2-4(1)(9+k2)≥0
.4-8k+4k2-36-4k2≥0
.-8k-32≥0
.-8k≥32
.-k≥4
.k≤-4 (shown)
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