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 given: \(x^2 + 8x + 16 = 0\).
2. Recall that the number and type of solutions of a quadratic equation can be determined using the discriminant, which is given by the formula \(\Delta = b^2 - 4ac\), where \(a\), \(b\), and \(c\) are the coefficients from the quadratic equation \(ax^2 + bx + c = 0\).
3. For the equation \(x^2 + 8x + 16 = 0\), identify the coefficients: \(a = 1\), \(b = 8\), and \(c = 16\).
4. Calculate the discriminant using the formula: \(\Delta = (8)^2 - 4 \times 1 \times 16\).
5. Analyze the value of the discriminant: if \(\Delta > 0\), there are 2 distinct real solutions; if \(\Delta = 0\), there is exactly 1 real solution (a repeated root); if \(\Delta < 0\), there are 2 imaginary (complex) solutions.