## Exam-Style Question on Quadratic Equations## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 118. This question is similar to one that appeared on a IGCSE Extended paper in 2014. The use of a calculator is allowed.

(a) Show that the equation \(\frac{3}{x+1}+\frac{3x-9}{2}=1\) can be simplified to \(3x^2-8x-5=0\).

(b) Solve the equation \(3x^2-8x-5=0\) showing all of your working and giving answers to three significant figures.

(c) The total surface area of a cone with radius \(x\) and slant height \(8x\) is equal to the area of a circle with radius r. Show that \(r = 3x\).

[The curved surface area, \(A\), of a cone with radius \(r\) and slant height \(l\) is \(A=\pi rl\).]

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