If one root of ∣∣
∣∣76x2x2x37∣∣
∣∣=0 is x =-9, find the other roots.
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Solution
∣∣
∣∣76x2x2x37∣∣
∣∣=7(7x−6)−2(42−3x)+x(12−x2) =49x−42−84+6x+12x−x3=−x3+18x+49x−42−84=−x3+67x−126 (x+9) will be One of the factors of given cubic. −x3+67x−126=(x+9)(−x2+9x−14)=(−1)(x+9)(x2−9x+14)=(−1)(x+9)(x2−9x+14)=(−1)(x+9)(x−7x−2x+14)=(−1)(x+9)(x−7)(x−2)=(x+9)(7−x)(x−2)=0∴x=−9,7,2