Derick wants to make a table which has an area of 10m^2. The length of the table must be 3m longer than the width. The equation that represent the equation is w(w+3)=10.
a. Without solving it, what should be the value of the discriminant of the equation? Is it positive or negative? Why?
b. Based on the value of the discriminant; how will you describe the dimensions of the table?
a positive discriminant means you have two real roots.
a. To determine the value of the discriminant of the equation, we need to consider the quadratic equation in the form of ax^2 + bx + c = 0, where a, b, and c are coefficients.
In this case, the equation representing the area of the table is w(w+3) = 10, which can be rearranged as w^2 + 3w - 10 = 0. Comparing it with the standard quadratic equation form, we have a = 1, b = 3, and c = -10.
The discriminant, denoted by Δ, is calculated as Δ = b^2 - 4ac. Substituting the values, we get Δ = 3^2 - 4(1)(-10) = 9 + 40 = 49.
Since the discriminant is a positive value (49), the answer to this part is that the discriminant is positive.
b. Based on the value of the discriminant, we can describe the dimensions of the table as follows:
1. If the discriminant is positive, it means there are two distinct real solutions for the equation. In this case, it suggests that there are two possible widths that satisfy the given conditions and result in an area of 10m^2.
2. Since the equation represents the area of the table, the positive discriminant indicates that the table can have two different dimensions with an area of 10m^2.