the set s={x|x2+4x-5=0}
To better understand the set S, let's first solve the equation x^2 + 4x - 5 = 0.
Step 1: Write the quadratic equation in standard form: x^2 + 4x - 5 = 0
Step 2: To solve this equation, we can use the quadratic formula, which states that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions (or roots) can be found using the formula: x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 1, b = 4, and c = -5. Substituting these values into the quadratic formula, we get:
x = (-4 ± √(4^2 - 4(1)(-5))) / (2(1))
x = (-4 ± √(16 + 20)) / 2
x = (-4 ± √36) / 2
x = (-4 ± 6) / 2
Step 3: We now have two possible solutions for x:
x1 = (-4 + 6) / 2 = 2 / 2 = 1
x2 = (-4 - 6) / 2 = -10 / 2 = -5
So the solutions to the quadratic equation x^2 + 4x - 5 = 0 are x1 = 1 and x2 = -5.
Step 4: Now, let's find the set S based on these solutions. The set S is defined as {x | x^2 + 4x - 5 = 0}. In our case, the solutions are x1 = 1 and x2 = -5. Therefore, the set S can be written as S = {1, -5}.