1.

If x = -3 is a zero of a polynomial x3 + 9x2 + 27x + k, find the value of k.

Answer»

Answer:

k = -3

Step-by-step explanation:

Given a cubic polynomial auch that,

{x}^{3} + 9 {x}^{2} + 27x + k

Also, it's given that,

On ONE of it's ZEREOS is -3.

To find the value of k.

We know that,

Zero of a polynomial satisfy the EQUATION of the given polynomial.

Therefore, when we will substitute, the value of x = -3 in the given Polynomial, it will be equal to zero.

Therefore, we will GET,

=> p(-3) = 0

Substituting the values, we get,

= > {( - 3)}^{3} + 9 {( - 3)}^{2} + 27( - 3) + k = 0 \\ \\ = > - 27 + 9(9) - 51 + k = 0 \\ \\ = > 81 - (2 7 + 51) + k = 0 \\ \\ = > 81 - 78 + k = 0 \\ \\ = > 3 + k = 0 \\ \\ = > k = - 3

Hence, the required value of k = -3.


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