If z i (where i = 1 , 2 , … … … . . 6 ) be the roots of the equation z 6 + z 4 - 2 = 0 , then ∑ i = 1 6 z i 4 is equal to

Question

If z i (where i = 1 , 2 , … … … . . 6 ) be the roots of the equation z 6 + z 4 - 2 = 0 , then ∑ i = 1 6 z i 4 is equal to, 4, 6, 8, 1 0

MARKS App · Accepted Answer

Let, z 2 = t ⇒ t 3 + t 2 - 2 = 0 ⇒ t - 1 t 2 + 2 t + 2 = 0 ⇒ t = 1 or t 2 + 2 t + 2 = 0 ⇒ t = 1 , - 1 ± i ⇒ z = ± 1 or z 2 = - 1 ± i ⇒ z 2 = 1 , 2 ⇒ z 4 = 1 , 2 ⇒ ∑ i = 1 6 z i 4 = 1 + 1 + 2 + 2 + 2 + 2 = 10

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