Rotation 90 clockwise about the origin (3,-4)

Mathematics

1 answer:

kotegsom [21]3 years ago

6 0

Answer:

(-4, -3)

Step-by-step explanation:

This transformation is given by

(x, y) ------> (y, -x)

So (3, -4) transforms to (-4, -3)

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defon

Answer:

$f(x)=x^5-6x^4+14x^3-24x^2+40x$

Step-by-step explanation:

<u>Given information</u>:

Polynomial function with real coefficients.
Zeros: 0, 2i and (3+i).

For any complex number $z=a+bi$ , the complex conjugate of the number is defined as $z^*=a-bi$ .

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if f(x) is a polynomial with real coefficients, and 2i is a root of f(x)=0, then its complex conjugate -2i is also a root of f(x)=0.

Similarly, if (3+i) is a root of f(x)=0, then its complex conjugate (3-i) is also a root of f(x)=0.

Therefore, the polynomial in factored form is:

$f(x)=ax(x-2i)(x-(-2i))(x-(3+i))(x-(3-i))$