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.

Given:

If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

To do:

We have to find whether the given statement is true or false.

Solution:

Let $\alpha, \beta$ and $\gamma$ be the zeroes of a cubic polynomial p(x).

Given that two of the zeroes are zero.

Let $\alpha=\beta=0$ and $\gamma=a$

Therefore,

$p(x)=(x-\alpha)(x-\beta)(x-\gamma)$

$=(x-0)(x-0)(x-a)$

$=x^{3}-a x^{2}$ which does not have linear and constant terms.

Hence, the given statement is true.

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Updated on: 10-Oct-2022

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