Question

If ax power n-1 + bx power n-2 + cx power n-3 is a cubic polynomial, where n belongs to N, then find the value of 'n'.
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Answer 1

Given : axⁿ⁻¹ +bxⁿ⁻²  + cxⁿ⁻³ is  a cubic polynomial where n belongs to N,

To Find : the value of 'n'

Solution:

axⁿ⁻¹ +bxⁿ⁻²  + cxⁿ⁻³ is  a cubic polynomial  

so maximum power to x should be 3

and one of the power to x should be 3

case 1 :  n - 1 = 3

=> n = 4

n - 2 = 4 - 2 = 2

n - 3 = 4 - 3 = 1

=> ax³ + bx²  + cx  

Hence n = 4

case 2 :

n - 2 = 3

=> n = 5

n - 1 = 4   > 3  Hence not a cubic polynomial

case 3 :

n - 3 = 3

=> n = 6

n - 1 = 5   > 3  Hence not a cubic polynomial

Value of n = 4

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