Questions: Solve the following quadratic equation by factoring. 7 x^2 - 20 x + 12 = 0 Select all correct answers. Select all that apply: 6/7 8/7 -8/7 2 9 1

Transcript text: Solve the following quadratic equation by factoring. \[ 7 x^{2}-20 x+12=0 \] Select all correct answers. Select all that apply: $\frac{6}{7}$ $\frac{8}{7}$ $-\frac{8}{7}$ 2 9 1

Solution

Solution Steps

To solve the quadratic equation by factoring, we need to express it in the form $(ax + b)(cx + d) = 0$. We will look for two numbers that multiply to $ac$ (the product of the coefficient of $x^2$ and the constant term) and add up to $b$ (the coefficient of $x$). Once factored, we can solve for the roots by setting each factor equal to zero.

Step 1: Factor the Quadratic Equation

We start with the quadratic equation: \[ 7x^2 - 20x + 12 = 0 \] We can factor this equation as: \[ (7x - 6)(x - 2) = 0 \]

Step 2: Set Each Factor to Zero

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