Polynomial with complex zeroes
You can view as many worked out examples as you want. First you are shown the question. Click Show Answer to view the answer. Click Show another Example to view another example. The best way to master mathematics is by practice. But practice requires time. If you don't have the time to practice, you can always view many practice problems completely worked out and become good at it too.
Level 1 Level 2 Level 3 Level 4 Level 5
Question

Find a polynomial equation of smallest degree with a zero at $x=3-5i$.

Complex zeroes of polynomials come in pairs. If $x=3-5i$ is a zero of the polynomial, then the conjugate $x=3+5i$ is a zero of the polynomial too.

Thus $(x-(3-5i))$ and $(x-(3+5i))$ are factors of the polynomial.

$(x-(3-5i))(x-(3+5i))$

$=((x-3)-(-5i))((x-3)+(-5i))$

$=x^{2}-6x+9+25$

$=x^{2}-6x+34$

$x^{2}-6x+34=0$ is one such polynomial equation