If begin mathsize 20px style alpha comma beta comma gamma space a r e space t h e space r o o t s space o f space t h e space e q u a t i o n space x cubed plus p x plus q equals 0 comma t h e n
space t h e space v a l u e space o f space t h e space d e t e r m i n a n t
open vertical bar table row cell alpha space end cell cell beta space end cell gamma row beta gamma alpha row gamma alpha beta end table close vertical bar space equals
i. q space space space space i i.0 space space space space i i i. p space space space space i v. p squared minus 2 p
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Asked by sunil2791 | 8th Jul, 2017, 07:37: PM

Expert Answer:

begin mathsize 16px style straight x cubed plus px plus straight q equals 0 rightwards double arrow straight x cubed plus 0 straight x squared plus px plus straight q equals 0
straight alpha plus straight beta plus straight gamma equals fraction numerator negative coefficient space of space straight x squared over denominator coefficient space of space straight x cubed end fraction equals 0
αβγ equals fraction numerator negative coefficient space of space straight x over denominator coefficient space of space straight x cubed end fraction equals straight p
Solving space determinant space we space get
3 αβγ minus open parentheses straight alpha cubed plus straight beta cubed plus straight gamma cubed close parentheses
equals 3 αβγ minus open square brackets open parentheses straight alpha plus straight beta plus straight gamma close parentheses open parentheses straight alpha squared plus straight beta squared plus straight gamma squared minus αβ minus βγ minus αγ close parentheses plus 3 αβγ close square brackets
equals 3 αβγ minus open parentheses 0 plus 3 αβγ close parentheses
equals 0

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Answered by Sneha shidid | 8th Jul, 2017, 10:47: PM