Chapter 1 Quadratic Equations In One Unknown Worksheet With Answers Page 13
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Quadratic Equations in One Unknown
Name :
1D
Date :
Mark :
1.4B Nature of Roots
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Key Concepts and Formulae
1. Discriminant ∆ = b
− 4ac
2
2.
Discriminant
∆ > 0
∆ = 0
∆ < 0
∆ = b
− 4ac
2
Nature of roots of
2 distinct
1 double
no real roots
+ bx + c = 0
2
ax
real roots
real root
Find the discriminant for each of the following quadratic equations and determine the nature of the
roots. (1 – 6)
+ 2x − 3 = 0
+ 8x − 21 = 0
2
2
1.
3.
x
6x
Solution
Solution
∆ = (
− 4(
2
−3
2
)
1
)(
)
∆ = 8
− 4(6)(−21)
2
= (
)
16
= 568
Q ∆ = ( > / = / < ) 0
Q ∆ > 0
∴ The equation has two distinct real roots.
∴ The equation has (
)
two distinct
real roots.
+ 10x + 1 = 0
2
4.
4x
− x + 10 = 0
2
2.
x
Solution
Solution
∆ = (−1)
− 4(1)(10)
2
∆ = 10
− 4(4)(1)
2
= −39
= 84
Q ∆ < 0
Q ∆ > 0
∴ The equation has no real roots.
∴ The equation has two distinct real roots.
13
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