Quadratic Equations: Variations
Case distinction
In the chapter Linear equations with one unknown we have seen how, in some cases, equations can be reduced to simpler equations, by factorization, or if the absolute value #|x|# of #x# occurs, differentiating between #x\ge0# and #x\lt0#. These cases also occur in quadratic equations.
#x=0\lor x=7\lor x= -3#
Because we can factorize the left hand side in two factors: #x\cdot (x^2-4x-21)#, the equation can be reduced to \[x=0\lor x^2-4x-21 = 0\tiny.\]Hence we need to solve the quadratic equation. The abc-formula gives # x=7\lor x= -3#. Hence the answer is #x=0\lor x=7\lor x= -3#.
Because we can factorize the left hand side in two factors: #x\cdot (x^2-4x-21)#, the equation can be reduced to \[x=0\lor x^2-4x-21 = 0\tiny.\]Hence we need to solve the quadratic equation. The abc-formula gives # x=7\lor x= -3#. Hence the answer is #x=0\lor x=7\lor x= -3#.
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