Area=3x2 +5x -2 FInd length and width of the rectangle
The expression factors as (3x-1)(x+2)
However, there are lots of other ways to divide things up. For example, if x=3, the area is 8*5 = 40, but those are not the only two ways to get two numbers which multiply to 40.
To find the length and width of a rectangle using the given expression for the area, we need to factorize the quadratic equation.
Area = (3x + 2)(x + 1)
To find the length and width, we compare the factors in the expression with the formula for a rectangle's dimensions, which is length × width.
Therefore, the length of the rectangle is 3x + 2, and the width of the rectangle is x + 1.
To find the length and width of the rectangle, you need to determine the roots of the given quadratic equation, which represents the area of the rectangle.
The equation is:
Area = 3x^2 + 5x - 2
We can factorize the equation to find its roots:
3x^2 + 5x - 2 = 0
To factorize, we look for two numbers whose product is equal to the product of the coefficient of the x^2 term (3) and the constant term (-2), and whose sum is equal to the coefficient of the x term (5).
The factors of 3 are 1 and 3, and the factors of -2 are -1 and 2. Now we check all possible combinations:
3x^2 + 6x - x - 2 = 0
(3x^2 + 6x) + (-x - 2) = 0
3x(x + 2) - 1(x + 2) = 0
(3x - 1)(x + 2) = 0
Now, applying the zero product property, either (3x - 1) = 0 or (x + 2) = 0.
For the first case, (3x - 1) = 0:
3x = 1
x = 1/3
For the second case, (x + 2) = 0:
x = -2
So, the roots of the equation are x = 1/3 and x = -2. These roots represent the length and width of the rectangle, respectively.
Therefore, the length of the rectangle is 1/3 and the width of the rectangle is -2. However, it is not possible to have a negative width for a rectangle, so we take the positive value only.
Thus, the length of the rectangle is 1/3 and the width of the rectangle is 2.