Question

There are many different methods for solving a quadratic equation, but not all of them will work for every method. For example, the equation 2x^2 - 12x + 20 = 0 has no real solutions.

A. Factoring and completing the square
B. Quadratic formula and graphing
C. Synthetic division and rational root theorem
D. Matrix method and substitution

Answer 1

The equation 2x^2 - 12x + 20 = 0 does not have any real solutions. The best method to find the solutions, even if they are not real, is the quadratic formula and graphing.

Step-by-step explanation:

The quadratic equation 2x^2 - 12x + 20 = 0 does not have any real solutions. This means that there are no values of x that satisfy the equation and make it true.

To determine this, you can use various methods for solving quadratic equations. For this specific equation, you can try factoring or completing the square, but neither method will give you real solutions.

Therefore, option A (Factoring and completing the square) would not work for this equation. Option B (Quadratic formula and graphing) is the best method to find the solutions, even if they are not real. Option C (Synthetic division and rational root theorem) and Option D (Matrix method and substitution) are not applicable to quadratic equations.