The area of a rectangular painting is given by the trinomial x^2 - 5x - 36 what are the possible dimensions of the painting use factoring
We need to find two numbers whose product is equal to -36 and whose sum is equal to -5. These numbers are -9 and 4. Therefore, we can rewrite the trinomial as (x-9)(x+4).
Since the length and width of the rectangle must have positive values, we can discard the negative value of x+4.
Therefore, the possible dimensions of the painting are x-9 and x+4, where x is a positive root of the equation x^2 - 5x - 36 = 0.
Using the quadratic formula, we get:
x = [5 ± sqrt(5^2 + 4(36))]/2
x = [5 ± 13]/2
x = 9 or x = -4
Since x must be positive, the only valid solution is x = 9.
Therefore, the possible dimensions of the painting are:
Length = x-9 = 0
Width = x+4 = 13
So, the dimensions of the painting are 0 units by 13 units, but this is not a valid rectangle. Therefore, there are no possible dimensions for the painting.