# Form 4 Add Math Chapter 2

**Topics:**Quadratic equation, Completing the square, Elementary algebra

**Pages:**2 (256 words)

**Published:**February 15, 2013

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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