Question

1. how many real solutions does $x^2 + 8x + 20 = 0$ have?

a. 0
b. 1
c. 2

Explanation:

Step1: Recall discriminant formula

For a quadratic equation \(ax^{2}+bx + c = 0\), the discriminant \(D=b^{2}-4ac\). If \(D>0\), two real solutions; \(D = 0\), one real solution; \(D<0\), no real solutions.

Step2: Identify coefficients

In \(x^{2}+8x + 20=0\), \(a = 1\), \(b = 8\), \(c = 20\).

Step3: Calculate discriminant

\(D=(8)^{2}-4\times1\times20=64 - 80=- 16\).

Step4: Analyze discriminant

Since \(D=-16<0\), the equation has 0 real solutions.

Answer:

A. 0