Question

An equation is shown. x2+4x+3=0
. Complete the statements.

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(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 \( x^2 + 4x + 3 = 0 \).

From this equation, we can identify the coefficients:

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

To find the solutions to the equation, we can either factor the quadratic or use the quadratic formula.

Factoring \( x^2 + 4x + 3 \):

1. Look for two numbers that multiply to \( c = 3 \) and add to \( b = 4 \). The numbers are \( 1 \) and \( 3 \).
2. So it factors to \( (x + 1)(x + 3) = 0 \).

Setting each factor to zero gives:

- \( x + 1 = 0 \) which means \( x = -1 \).
- \( x + 3 = 0 \) which means \( x = -3 \).

Therefore, one solution to the equation is **-1** (or you can also use -3 as another valid solution).

Summary:

- 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**.