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Question

If one root of ∣ ∣76x2x2x37∣ ∣=0 is x =-9, find the other roots.
 


Solution

∣ ∣76x2x2x37∣ ∣=7(7x6)2(423x)+x(12x2)
=49x4284+6x+12xx3=x3+18x+49x4284=x3+67x126
(x+9) will be One of the factors of given cubic.

x3+67x126=(x+9)(x2+9x14)=(1)(x+9)(x29x+14)=(1)(x+9)(x29x+14)=(1)(x+9)(x7x2x+14)=(1)(x+9)(x7)(x2)=(x+9)(7x)(x2)=0x=9,7,2

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