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 coefficients of the quadratic equation \(x^2 + 8x + 16 = 0\). Here, \(a = 1\), \(b = 8\), and \(c = 16\).
2. Recall that the number and type of solutions of a quadratic equation can be determined using the discriminant formula: \(\Delta = b^2 - 4ac\).
3. Calculate the discriminant by substituting the values: \(\Delta = (8)^2 - 4 \times 1 \times 16\).
4. Analyze the value of 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.
5. Based on the discriminant value, conclude the number and type of solutions without solving the equation.