AS level	Pure Maths C1 --------------------- Quadratic Formula This is all about finding if a Quadratic equation has 0, 1 or 2 roots.	A Revision Aid
	This takes the co-efficients of the quadratic equation and tells you about it's roots. The Quadratic formula is as follows b2 - 4ac So all you need to do is identify the a, b and c, co-efficients plug them into this formula and then look to see whether it is ... < 0 = No roots = 0 = 1 root >0 = 2 roots easy, peasy init !! Example: Determine how many roots the following equation has x2 + (2k + 1)x + (k2 + k + 1) = 0 so ... a = 1, b = (2k + 1) and c = (k2 + k + 1) We plug these into the Quadratic formula to get .. (2k + 1)2 - 4 x 1 x (k2 + k + 1) expanded to 4k2 + 4k + 1 - 4k2 - 4k  - 4 simplified to - 3 and as -3 is < 0 we can say that x2 + (2k + 1)x + (k2 + k + 1) = 0 has NO ROOTS Done !!!	notes A "normal" is another name for a perpendicular line from a tangent.
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