Question

find x value of determinant |(x 3 7) (2 x 2) (7 6 x )|=0​

Answer 1

Answer:

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Answer 2

$Solution : </p><p></p><p>Since ∣∣∣∣x273x672x∣∣∣∣=0|x372x276x|=0</p><p>Expanding along R1R1</p><p>x(x2−12)−3(2x−14)+7(12−7x)=0x(x2-12)-3(2x-14)+7(12-7x)=0</p><p>⇒x3−12x−6x+42+84−49x=0⇒x3-12x-6x+42+84-49x=0</p><p>⇒x3−67x+126=0⇒x3-67x+126=0………………i</p><p>Here 126×1=9×2×7126×1=9×2×7</p><p>For x=2,23−67×2+126=134−134=0x=2,23-67×2+126=134-134=0</p><p>Hence x=2x=2 is a root.</p><p>For x=7,63−67×7+126=469−169=0x=7,63-67×7+126=469-169=0</p><p>Hence x=7x=7 is also a root.</p><p></p><p>$