Find the roots of each quadratic polynomial.
1. x^2 + 2
2. x^2 - 6x - 7
1. x^2 = -2
x = +/- i sqrt 2 imaginary roots
2. x = [ 6 +/- sqrt (36+28) ] / 2
= 3 +/- 4
7 or -1
or just factor it
(x-7)(x+1) = 0
I'm sorry, but I don't understand. I haven't learned about this solving method yet. What are imaginary roots?
If you have not learned about imaginary roots then you have a typo in number 1
You can not solve
x^2 = -2
Unless you have had complex numbers.
You can do number two the second way I did it, by factoring.
I haven't learned to factor quadratic equations yet, either. In my current lesson, I'm learning to solve quadratic equations by graphing. However, I am struggling to grasp the concept. Thus, what is a simple way to find the roots of quadratic equations by graphing?
To find the roots of a quadratic polynomial, we can use the quadratic formula or factorization.
1. For the quadratic polynomial x^2 + 2, let's use the quadratic formula:
The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / 2a
For this polynomial, a = 1, b = 0, and c = 2.
Plugging the values into the quadratic formula, we get:
x = (0 ± √(0^2 - 4(1)(2))) / 2(1)
Simplifying further:
x = (0 ± √(-8)) / 2
The square root of -8 is not a real number because it involves an imaginary number (i.e., the square root of -1). Therefore, this polynomial does not have real roots.
2. For the quadratic polynomial x^2 - 6x - 7, let's use factorization:
This quadratic polynomial can be factored as:
(x - 7)(x + 1) = 0
Setting each factor equal to zero gives us the solutions:
x - 7 = 0 or x + 1 = 0
Solving each equation:
For x - 7 = 0, add 7 to both sides:
x = 7
For x + 1 = 0, subtract 1 from both sides:
x = -1
Therefore, the roots of the quadratic polynomial x^2 - 6x - 7 are x = 7 and x = -1.