Multiple Choice
Determine the number and type of solutions of the given quadratic equation. Do not solve.
1. Equations and Inequalities
The Quadratic Formula
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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 standard form: \( ax^2 + bx + c = 0 \). In this case, \( a = 1 \), \( b = 8 \), and \( c = 16 \).
Calculate the discriminant \( \Delta \) using the formula \( \Delta = b^2 - 4ac \).
Substitute the values of \( a \), \( b \), and \( c \) into the discriminant formula: \( \Delta = 8^2 - 4 \times 1 \times 16 \).
Simplify the expression to find the value of the discriminant.
Determine the number and type of solutions based on the discriminant: If \( \Delta > 0 \), there are 2 real solutions; if \( \Delta = 0 \), there is 1 real solution; if \( \Delta < 0 \), there are 2 imaginary solutions.
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