Open Question
In Exercises 127–130, solve each equation by the method of your choice.1/(x^2 - 3x + 2) = 1/(x + 2) + 5/(x^2 - 4)
1. Equations & Inequalities
The Quadratic Formula
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Determine the number and type of solutions of the given quadratic equation. Do not solve.
A
2 real solutions
B
1 real solution
C
2 imaginary solutions
Verified step by step guidance1
Identify the quadratic equation in the standard form: \( ax^2 + bx + c = 0 \). In this case, \( a = 1 \), \( b = 8 \), and \( c = 16 \).
Use the discriminant formula \( b^2 - 4ac \) to determine the nature of the solutions. The discriminant helps us understand how many and what type of solutions the quadratic equation has.
Calculate the discriminant: \( b^2 - 4ac = 8^2 - 4 \times 1 \times 16 \).
Interpret the discriminant: If \( b^2 - 4ac > 0 \), there are 2 distinct real solutions. If \( b^2 - 4ac = 0 \), there is exactly 1 real solution (a repeated root). If \( b^2 - 4ac < 0 \), there are 2 complex (imaginary) solutions.
Based on the calculated discriminant, determine the number and type of solutions for the quadratic equation \( x^2 + 8x + 16 = 0 \).
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