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0 votes
14.1k views
in Mathematics by (59.7k points)

Number of roots of the equation z 10 – z5 – 992 = 0 with real part negative is: 

(A) 3 

(B) 4 

(C) 5 

(D) 6 

1 Answer

+1 vote
by (56.9k points)
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Best answer

Correct option is (C)

Explanation :

Z 10 – Z 5 = 992  

Z 5 (Z5 – 1) = 32(31)

Z 5 = t 

⇒ t 2 – t = 992  

⇒ t 2 – 32t + t – 992 = 0 

⇒ t = 32, –31 ⇒ Z 5 = 32, –31 

⇒ Z5 = 32 has 2 roots with –ve real coeff. and Z 5 = –31 has 3 roots with –ve real coeff.

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