Question

Part of the roof of a factory is devoted to mechanical support and part to green space. The area G that is designated as green space can be modeled by the polynomial 2x2 - 7x and the area M that is devoted to mechanical support can be modeled by the polynomial x2 - 9x + 24. Given that the area R of the roof is 36 square yards, write and solve a quadratic equation to find the total area of the green space. **Use the positive value for your solution.

Answer 1

We have been given that part of the roof of a factory is devoted to mechanical support and part to green space. The area G that is designated as green space can be modeled by the polynomial
`2x^2-7x` and the area M that is devoted to mechanical support can be modeled by the polynomial
`x^2-9x+24`.

We are asked to find the area of the green space, when area of roof (R) is 36 square yards.

The area of roof would be equal to sum of areas of green space and mechanical support.

`R=G+M`

`36=2x^2-7x+x^2-9x+24`

Let us solve for x.

`36=3x^2-16x+24`

`36-36=3x^2-16x+24-36`

`0=3x^2-16x-12`

`3x^2-16x-12=0`

`3x^2+2x-18x-12=0`

`x(3x+2)-6(3x+2)=0`

`(3x+2)(x-6)=0`

`(3x+2)=0,(x-6)=0`

`x=-(2)/(3),x=6`

Since length cannot be negative, therefore, the value of x would be 6.

The area of green space would be:

`2x^2-7x=2(6)^2-7(6)=72-42=30`

Therefore, the area of green space would be 30 square yards.