Quadratic Equations Worksheet With Answer Key
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7Ninth week lessons
Quadratic Equations (continued)
(Divided into 3 lectures of 50 minutes each)
Lecture – 25 (50 minutes)
a) Nature of roots of a quadratic equation.
b) Relation between roots and coefficients.
c) Class works
A. Nature of roots of a quadratic equation.
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The nature of the roots of a quadratic equation ax
+ bx + c = 0, a ≠ 0 depends
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upon the value of the expression ∆ = b
- 4ac, called the discriminant.
The following cases arise (for a, b, c rational numbers).
Case I : When ∆ > 0 and not a perfect square, the roots are unequal and irrational.
Case II When ∆ > 0 and a perfect square, the roots are rational and unequal.
Case III when ∆ = 0, the roots are rational and equal.
Case IV when ∆ < 0, the roots are unequal and imaginary.
Example1:
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Write the nature of roots of 2x
+ 3x - 5 = 0
Solution:
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Comparing the given equation with ax
+ bx + c = 0, we get
a = 2, b = 3 and c = -5.
Now
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∆ = b
- 4ac
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= (3)
– 4. 2. (-5)
= 9 + 40
= 49
2
=(7)
> 0. Here we got the final result as a perfect square and positive. So
it indicates that the given equation must give two roots which are rational and
unequal.
Example2:
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Write the nature of roots of 2x
+ 3x - 4 = 0
Solution:
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Comparing the given equation with ax
+ bx + c = 0, we get
a = 2, b = 3 and c = -4.
Now
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∆ = b
- 4ac
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