Solve the equation. (Find only the real solutions.)
x2 - x - 2 = 0
they also said there is a smaller value and a larger value ??
(x-2)(x+1) = 0
now, if the product of two numbers is zero, one of the numbers must be zero. So, which value of x makes each factor zero?
To solve the equation x^2 - x - 2 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Let's apply this formula to our equation:
Here, a = 1, b = -1, and c = -2.
x = (-(-1) ± √((-1)^2 - 4(1)(-2))) / (2(1))
= (1 ± √(1 + 8)) / 2
= (1 ± √9) / 2
= (1 ± 3) / 2
We have two solutions:
1. When x = (1 + 3) / 2 = 4 / 2 = 2
2. When x = (1 - 3) / 2 = -2 / 2 = -1
So, the real solutions to the equation x^2 - x - 2 = 0 are x = 2 and x = -1.
The "smaller value" and "larger value" mentioned in the question may refer to the order of these solutions on the number line. Therefore, the smaller value is -1, and the larger value is 2.