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Quadratic Formula

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This item is taken from IGCSE Mathematics (0580) Paper 43 of October/November 2010.

To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Algebra
   (b) Specific topic: The Quadratic Formula

   (c) Formula Needed:

IGCSE,mathematics,Cambridge,CIE,examination,past papers,algebra,solutions,unknown,variables,quadratic equations,factoring,square root,decimals
Let us take note that the given is a quadratic equation but it is not factorable. We can then find the solution(s) of the equation by using the quadratic formula.

Let us first identify the values of a, b and c for the quadratic formula.
IGCSE,mathematics,Cambridge,CIE,examination,past papers,algebra,solutions,unknown,variables,quadratic equations,factoring,square root,decimals
We can now substitute the values of a, b and c in the formula:
IGCSE,mathematics,Cambridge,CIE,examination,past papers,algebra,solutions,unknown,variables,quadratic equations,factoring,square root,decimals
At this point, we should not get the decimal value first of the square root of 17. Leave it as is. 

We can now separate the solution into two, separating the "+"and "-" signs, then simplify.
IGCSE,mathematics,Cambridge,CIE,examination,past papers,algebra,solutions,unknown,variables,quadratic equations,factoring,square root,decimals
Therefore, the solutions for the equation is x = -0.22 or x = -2.28.

*We should take note also that the complete working is required in this item. The most important part of it is the correct quadratic formula with correct values of a, b and c.

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