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  • Are the following statements ‘True’ or ‘False’? Justify your answers. If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

Are the following statements ‘True’ or ‘False’? Justify your answers. If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

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Answer.          [True]

Polynomial: It is an expression of more than two algebraic terms, especially then sum of several terms that contains different powers of the same variable(s).

Cubic polynomial: when the degree of polynomial is three then the polynomial is called cubic polynomial.

Let \alpha _1 , \alpha _2 ,\alpha _3 be the zeroes of a cubic polynomial.

It is given that two of the given zeroes have value zero.

i.e. \alpha _1 = \alpha _2 = 0

Let p(y) = (y - \alpha _1)(y - \alpha _2)(y -\alpha _3)

p(y) = (y - 0) (y - 0) (y - \alpha _3)

p(y) = y^3 y^2\alpha _3

Here, we conclude that if two zeroes of a cubic polynomial are zero than the polynomial does not have linear and constant terms.

Hence, given statement is true.

 

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