Multiple Choice
Which mathematician is most commonly credited with introducing a general method equivalent to the modern quadratic formula for solving equations of the form ?
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1. Equations & Inequalities
The Quadratic Formula
Multiple 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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