Question

solve the quadratic trinomial: $x^2 + 5x + 6 = 0$.
options:
x=1,x=6
x=-1,x=-6
x=2,x=3
x=-2,x=-3

Explanation:

Step1: Factor the quadratic trinomial

We need to factor \(x^{2}+5x + 6 = 0\). We look for two numbers that multiply to \(6\) (the constant term) and add up to \(5\) (the coefficient of \(x\)). The numbers \(2\) and \(3\) satisfy this because \(2\times3 = 6\) and \(2 + 3=5\). So, we can factor the trinomial as \((x + 2)(x+3)=0\).

Step2: Solve for \(x\)

Using the zero - product property, if \((x + 2)(x + 3)=0\), then either \(x+2 = 0\) or \(x + 3=0\).

• If \(x+2=0\), then \(x=-2\).
• If \(x + 3=0\), then \(x=-3\).

Answer:

\(x=-2,x = - 3\) (the option with \(x=-2,x=-3\))