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2015-09-18T21:23:35+08:00

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The cubic formula in simplest form To solve the cubic equation (1) 3 2 y py qy r + + += 0 we must first remove the quadratic term. This is always achieved with the substitution (2) 3 p y x = − . Substituting (2) into (1) we get (3) 3 x cx a − −= 3 20 , where (4) 2 9 3 p q c = − and 3 6 27 2 pq p r a = −− . (Equation (3) is known as the reduced cubic.) Now we can write our cubic formula for the real root of (3). 
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