Nature of roots (Theory, Exercises and Answers)

Nature of roots (Theory, Exercises
and Answers)
 To determine the actual roots
−b ± √ b −4 ac
2
x=
2a
 To determine the nature of roots
2
∆=b −4 ac Discriminant

2
∆=b −4 ac Nature of roots
∆≥0
Real
∆ <0
Non - Real
∆ Perfect square Rationale
∆ not ʼn completely square Irrational
∆=0
Equal
∆≠0
Uneven


 Note: Equation must be written in standard form
 GRAPHIC SPOKEN

2
∆=b −4 ac On the graph
∆ >0 Two unequal x-sections
∆=0 Touch the x-axis
∆ <0 No x-sections



−b
 Note: give x - coordinate of turning point
2a
 To determine unknown values
o Real roots ∆≥0
o Non - Real roots ∆ <0
o Equal roots ∆=0

, o Rational roots ∆ Perfect square
o Real and uneven roots ∆ >0
 Example:
For which value (s) of K will x 2+ kx +2 k=0 have real roots?




Exercises
1. Describe the nature of the roots of a quadratic equation in full, if
a. ∆=12
b. ∆=−3
c. ∆=16
d. ∆=0
2. Draw a sketch graph of y=ax 2+ bx+ c if….
a. ∆=21 en a> 0
b. ∆=3 en a< 0
c. ∆=16 en a< 0
d. ∆=0 en a>0