Two roots of the cubic $ x^{3}+3 x^{2}+k x-12=0 $ are real and unequal but have the same absolute value. Then the value of $ \mathrm{k} $ is

Question

Two roots of the cubic $ x^{3}+3 x^{2}+k x-12=0 $ are real and unequal but have the same absolute value. Then the value of $ \mathrm{k} $ is, $ 4 $, $ -4 $, $ 6 $, $ -9 $

MARKS App · Accepted Answer

Let the roots are r , - r and t Hence, r - r + t = - 3 ⇒ t = - 3 Now, product of the roots is ( r ) ( - r ) ( t ) = 12 ⇒ - r 2 ( - 3 ) = 12 ⇒ r 2 = 4 Hence, roots are 2 , - 2 and - 3 Now, sum of the product taken two at a time is r ( - r ) + ( - r ) t + t r = k ⇒ - 4 - 6 + 6 = k ⇒ k = - 4

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