Form 4 Add Math Chapter 2

Topics: Quadratic equation, Completing the square, Elementary algebra Pages: 2 (256 words) Published: February 15, 2013
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
* Forming quadratic equation from given roots
SOR=sum of roots POR=product of roots
SOR=-ba POR=ca
* 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:
.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
.k≤-4 (shown)
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • BIOLOGY form 4 chapter 2 Essay
  • Add Math Essay 2
  • Essay about add math project
  • Essay about add math syllabus
  • Add Math Project Work 2 Essay
  • Case # 4 Chapter 2. Essay
  • Essay about Consumer Math test 2

Become a StudyMode Member

Sign Up - It's Free