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 2x2−12x+20=0 has no real solutions.

Explain in your own words why you cannot use the FACTORING method to solve this equation.

Answer 1

The equation 2x^2-12x+20=0 cannot be solved by factoring because it has a negative discriminant, indicating that there are no real solutions to factor into real-numbered binomials. Instead, the quadratic formula must be used to find the complex roots.

Step-by-step explanation:

The equation 2x^2−12x+20=0 is a quadratic equation, which is a type of second-order polynomial. Factoring is a method used to solve quadratic equations when the equation can be broken down into two binomial expressions that, when multiplied together, give the original quadratic equation. However, not all quadratic equations can be factored easily, especially when they do not have real solutions. In the case of 2x^2−12x+20=0, factoring it into real-numbered binomials is not possible because the discriminant (b^2 - 4ac) is negative, indicating that there are no real roots. Instead, we can use the quadratic formula to find the complex roots for this equation.