Question

verify that 3 -1 -1/3 are thr zeros of the cubic polynomial p(x) =3x3-5x2-11x-3 and then verify the relationship between the zeros and its coefficient

Answer 1

Heya !!!




P(X) = 3X³ - 5X² -11X - 3




P(3) = 3 × (3)³ - 5 × (3)² - 11 × 3 -3





=> 3 × 27 - 5 × 9 - 33 -3




=> 81 - 45 -36


=> 81 - 81 = 0


Remainder = 0


It means 3 is a zero of the given polynomial.

P( X ) = 3X³ -5X² -11X -3



Here,




A = 3 , B = -5 , C = -11 and D = -3



Sum of zeroes = -B/A = -5/3



And,



Product of zeroes = -D/A = 3/3 = 1



(2) P(-1)




P(-1) = 3 × (-1)³ -5 × (-1)² -11 × -1 -3



=> 3 × -1 - 5 × 1 + 11 -3



=> -3 - 5 + 8



=> -8+8 = 0



REMAINDER = 0


It means -1 is a zero of the given polynomial.




(3) P (-1/3)



Same as (1) and (2).





HOPE IT WILL HELP YOU....... :-)

Answer 2

Heya mate,

here is your answer,

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● Verifying zeroes :-

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=> At x = 3 ,

Since p (3) = 0

Hence , 3 is zero of p (x)

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=> At x = -1

Since p (-1) = 0

Hence , -1 is zero of p (x)

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=> At x = -1/3

Since p (-1/3) = 0

Hence, -1/3 is zero of p (x)

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● Verifying relationship between zeroes and coefficients

thanks !!!!

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