how do you find the root(s) of the equation x^2+3x-4=0
To find the roots of the equation x^2 + 3x - 4 = 0, you can use the quadratic formula.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation x^2 + 3x - 4 = 0, we have a = 1, b = 3, and c = -4. Let's substitute these values into the quadratic formula:
x = (-3 ± √(3^2 - 4(1)(-4))) / (2(1))
Simplifying this expression:
x = (-3 ± √(9 + 16)) / 2
x = (-3 ± √25) / 2
Now, we have two possible solutions:
x = (-3 + 5) / 2 = 2/2 = 1
x = (-3 - 5) / 2 = -8/2 = -4
Therefore, the equation x^2 + 3x - 4 = 0 has two roots: x = 1 and x = -4.