Question
Determine the nature of the roots of the following: a. 25π₯2 + 10π₯ + 1 = 0 b. 3π₯2 β 12 = 0 3
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Answer to a math question Determine the nature of the roots of the following: a. 25π₯2 + 10π₯ + 1 = 0 b. 3π₯2 β 12 = 0 3
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4.998 Answers
Solution:
1. For equation a.25x^2 + 10x + 1 = 0
- Identify coefficients:a = 25 b = 10 c = 1
- Calculate the discriminant:\Delta = b^2 - 4ac
\Delta = 10^2 - 4 \cdot 25 \cdot 1
\Delta = 100 - 100
\Delta = 0
The discriminant is 0, which means the quadratic equation has one real and repeated root.
2. For equation b.3x^2 - 12 = 0
- Identify coefficients:a = 3 b = 0 c = -12
- Calculate the discriminant:\Delta = b^2 - 4ac
\Delta = 0^2 - 4 \cdot 3 \cdot (-12)
\Delta = 0 + 144
\Delta = 144
The discriminant is positive, which means the quadratic equation has two distinct real roots.
1. For equation a.
- Identify coefficients:
- Calculate the discriminant:
The discriminant is 0, which means the quadratic equation has one real and repeated root.
2. For equation b.
- Identify coefficients:
- Calculate the discriminant:
The discriminant is positive, which means the quadratic equation has two distinct real roots.
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