mathleaks.com mathleaks.com Start chapters home Start History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
Expand menu menu_open Minimize
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }} # Using the Quadratic Formula to find Complex Roots

## Exercise 1.10 - Solution

a
In the Quadratic Formula, is the discriminant. Let's first rewrite the given equation in standard form. Having rewritten the equation, we can identify the values of and Now, let's evaluate the discriminant.
Simplify
The discriminant is
b

We want to use the discriminant of the given quadratic equation to determine the number and type of the roots. If we don't want to know the exact values of the roots, we only need to work with the discriminant. From Part A, we know that the discriminant of the given equation is Since the discriminant is greater than zero and a perfect square, the quadratic equation has two rational roots.

c
We will use the Quadratic Formula to find the exact solutions of the given equation. Recall that we have already identified the values of and in Part A, as well as the discriminant, Let's substitute these values into the Quadratic Formula.
Simplify
The solutions for this equation are Let's separate them into the positive and negative cases.

Using the Quadratic Formula, we found that the solutions of the given equation are and