Give a polynomial of degree 3 that has zeros of 18, 10i, and −10i, and has a value of −3434 when x=1. Write the polynomial in standard form axn+bxn−1+….

The polynomial in standard form is:

The zeros of the polynomial are 18, 10i and -10i.

So, the polynomial is:

Open bracket

Apply difference of two squares

Expand

In complex numbers, i^2 = -1.

So, we have:

Expand

From the question, P(1) = -34.

So, we have:

Divide both sides by -17

Make (a) the subject

Substitute in

Expand

Open bracket

Hence, the polynomial in standard form is:

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Given:

Polynomial of degree 3 that has zeros of 18, 10i, and −10i, and has a value of −34 when x=1.

To find:

The polynomial in standard form.

Solution:

If c is a zero of a polynomial then (x-a) is a factor of that polynomial.

18, 10i, and −10i are zeroes, so (x-18), (x-10i) and (x+10i) respectively are the factors of given polynomial.

So, the three degree polynomial is

where, a is a constant.

      ...(i)

The value of P(x) is -34 at x=1.

Divide both sides by 1717.

Put this value in (i).

Therefore, the required polynomial is .

answer: 2530

hope this

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column