This week in Precal we learned another method that we can use to solve quadratic equations, as well as learning about discriminant, and also learning on which method we can use to solve equations in the most efficient and smarter way through observing an equation.
The three methods that we learned so far from last week are:
- Square rooting
- Factoring or Zero Product Law
- Completing the Square
And from this week, we learned about the fourth method, which is called the Quadratic Formula. This formula can actually be used for any quadratic equations as long as we know the value of the coefficients and constants in a quadratic equation which are a, b, and c from this form of equation: ( + bx + c = 0) Furthermore, the quadratic formula is kind of like a short cut from completing the square method in which I will show you why…
The Quadratic Formula:
Example: +11x + 9 = 0
First of, we compare the example equation with + bx + c = 0
Then we get the values of a, b, and c. So,
a = 1
b = 11
c = 9
Discriminant – is a way that helps us predict the nature of the roots whereas it tells how many solutions and what kind of solutions we are going to get when we solve quadratic equations.
The discriminant is the – 4ac in the quadratic formula.
Without having to solve a quadratic equation, we can determine whether the equation has one, two, or no real roots. We can do this by substituting the values of a, b, and c into the discriminant and simplify to check the nature of its root.
Here’s the summary about Discriminant:
Since there are four methods we can use to solve equations, we should be observant when looking at quadratic equations, since we want to be efficient as possible when solving equations.
Square root method – we can use this method when there’s only one variable in a quadratic equation.
Factor / zero product law – we can use this method when a quadratic equation is factorable. To check if it’s factorable we multiply the first term by the last term/constant number and get its factors that sums up to the middle term. Furthermore, this can be used when there’s two variables and factorable.
Complete the square method – we can use this method when a quadratic equation is not factorable by checking first, and also, this actually works even the equation is factorable but, this is time consuming, so this is more like a backup method.
Quadratic Formula method – this formula actually came from completing the square method. We can use this formula for all kinds of quadratic equations however, it’s a little time consuming. So, preferably we use this when an equation is not factorable.