Can you explain how you would find out if one or both factors are really equal to 0?
To find out if one or both factors are equal to 0, you would need to solve the given equation. The equation should be in the form of a quadratic equation, which can be written as:
ax^2 + bx + c = 0
To solve this equation, you can apply the quadratic formula, which states that the solutions to the equation ax^2 + bx + c = 0 are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
To determine if one or both factors are equal to 0, you need to find the values of x when the equation is equal to 0. You can substitute 0 for the equation, resulting in:
0 = (-b ± √(b^2 - 4ac)) / (2a)
To simplify, you can multiply both sides of the equation by 2a, leading to:
0 = -b ± √(b^2 - 4ac)
Squaring both sides, you get:
0 = b^2 - 4ac
If the discriminant (b^2 - 4ac) is positive, then there are two distinct solutions, indicating that both factors are not equal to 0. If the discriminant is equal to 0, there is a single solution, suggesting that one factor is equal to 0. If the discriminant is negative, there are no real solutions, meaning that both factors are not equal to 0.
In summary, by applying the quadratic formula and analyzing the discriminant, you can determine if one or both factors are equal to 0.