Determine the number and type of solutions of the given quadratic equation. Do not solve. 
$x^2+8x+16=0$

• A. 2 real solutions
• B. 1 real solution
• C. 2 imaginary solutions

Answer: (B)

Verified step by step guidance

1. Identify the quadratic equation in the standard form: \( ax^2 + bx + c = 0 \). In this case, \( a = 1 \), \( b = 8 \), and \( c = 16 \).
2. 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.
3. Calculate the discriminant: \( b^2 - 4ac = 8^2 - 4 \times 1 \times 16 \).
4. 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.
5. Based on the calculated discriminant, determine the number and type of solutions for the quadratic equation \( x^2 + 8x + 16 = 0 \).