8. An equation is shown. x2+4x+3=0

Question

2
+
4

+
3
=
0
. Complete the statements.(4 points)
The value of a is
.

The value of b is
.

The value of c is
.

One solution to the equation is
.

Answer 1

The given equation is \(x^2 + 4x + 3 = 0\).

To complete the statements:

1. The value of \(a\) is 1 (coefficient of \(x^2\)).
2. The value of \(b\) is 4 (coefficient of \(x\)).
3. The value of \(c\) is 3 (constant term).

To find one solution to the equation, we can factor it:

The equation can be factored as \((x + 1)(x + 3) = 0\).

Setting each factor equal to zero gives:

1. \(x + 1 = 0 \rightarrow x = -1\)
2. \(x + 3 = 0 \rightarrow x = -3\)

Therefore, one solution to the equation is -1 (you could also state -3 as another solution, but since only one is requested, we give -1).

So, the completed statements are:

• The value of \(a\) is 1.
• The value of \(b\) is 4.
• The value of \(c\) is 3.
• One solution to the equation is -1.