Questions: Solve the quadratic function by factoring 12x^2+22x=0 a. x=0 and x=-11 / 6 b. x=0 and x=11 / 6 c. x=11 / 6 d. x=0 and x=-6 / 11

Solution Steps

To solve the quadratic equation \(12x^2 + 22x = 0\) by factoring, we first factor out the greatest common factor from the terms. This will allow us to express the equation as a product of two factors set to zero. We then solve for \(x\) by setting each factor equal to zero.

The given quadratic equation is \(12x^2 + 22x = 0\). We start by factoring out the greatest common factor, which is \(2x\). This gives us: \[ 2x(6x + 11) = 0 \]

To find the solutions, we set each factor equal to zero:

1. \(2x = 0\)
2. \(6x + 11 = 0\)

Solving these equations, we get:

1. \(x = 0\)
2. \(6x + 11 = 0 \Rightarrow 6x = -11 \Rightarrow x = -\frac{11}{6}\)

Final Answer