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Answers & Comments
1. x² - 6x - 27
a = 1
b = -6
c = -27
D = 144
Nature = rational
2. x² - 25
a = 1
b = 0
c = -25
D = 100
Nature = rational
3. x² + 10x + 25
a = 1
b = 10
c = 25
D = 0
Nature = Real and equal
4. 2x² - 5x + 3
a = 2
b = -5
c = 3
D = 1
Nature = Real and Unequal
The Discriminant
The quantity b² - 4ac is called the discriminant of the equation
Condition:
a) Real and Unequal if and only if b² - 4ac is "positive"
b) Real and Equal b² - 4ac is "zero"
c) Imaginary and Uneqaul b² - 4ac is "negative"
d) Rational b² - 4ac is "perfect square"
Explanation for the answers above:
1. The nature of the discriminant for number 1 is rational because the discriminant is 144 which is a perfect square of 12.
2. 1. The nature of the discriminant for number 2 is rational because the discriminant is 100 which is a perfect square of 10.
3. The nature of the discriminant for number 3 is real and equal because the discriminant is 0.
4. The nature of the discriminant for number 4 is real and unequal because the discriminant is 1 which is a positive number.
To learn more about discriminants, click the link below:
brainly.ph/question/5079201
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Step-by-step explanation:
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