if alpha beta and gamma are the zeroes of polynomial 6x3+3x2-5x+1 then find the value of alpha raised to -1+beta raised to -1+gamma raised to -1
Answer:
We have , And are the zeros of cubic polynomial 6x3 + 3x2 - 5x + 1
We know by the relationship between zeros and coefficient of a cubic polynomial , is
Sum of zeros =
+ + =
+ + = ------------------- ( 1 )
Sum of the products of zeros taken two at a time =
+ + = --------------------- ( 2 )
Product of zeros =
= --------------------- ( 3 )
Now for value of
-1 + -1 + -1
We can simplify it As :
Taking L.C.M. and get
Now substitute values from equation 2 and 3 we get
-1 + -1 + -1 = 5 ( Ans )
We have , And are the zeros of cubic polynomial 6x3 + 3x2 - 5x + 1
We know by the relationship between zeros and coefficient of a cubic polynomial , is
Sum of zeros =
+ + =
+ + = ------------------- ( 1 )
Sum of the products of zeros taken two at a time =
+ + = --------------------- ( 2 )
Product of zeros =
= --------------------- ( 3 )
Now for value of
-1 + -1 + -1
We can simplify it As :
Taking L.C.M. and get
Now substitute values from equation 2 and 3 we get
-1 + -1 + -1 = 5 ( Ans )