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

Answer 1

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

Explanation:

The area G that is designated as green space can be modeled by the polynomial
`2x^2-7x`

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`

`G = 2x^2 -7x M = x^2 -9x +24`

the total area is given by 36 yd^2. And we know that:

`R = 36 yd^2 = G+M`

Replacing the info given we got:

`36 = 2x^2 -7x +x^2 -9x +24\\\\ 12= 3x^2 -16 x`

And we can rewrite this expression like this:

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

And we can use the quadratic formual to solve this problem:

`X =(-b \pm √(b^2 -4ac))/(2a)`

With a = 3, b = -16 , c =-12. Replacing we have

`x = (16 \pm √((-16)^2 -4*(3)*(-12)))/(2*3)`

And the solutions for this case are:

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

The area of green space would be:

x = 6

`2x^2-7x\Rightarrow 2(6)^2-7(6)\\\\2x^2-7x=2(36)-42\\\\2x^2-7x=72-42\\\\2x^2-7x=30`

the area of green space would be 30 square yards.