0
$\begingroup$

I have learnt the if the discriminant of a polynomial is less than 0, then the polynomial has complex conjugate roots. I am trying to find a function for a quartic polynomial with a quadratic factor and complex conjugate roots. How do you find the discriminant of a quartic polynomial? I have only been familiarised with the discriminant of a quadratic.

$\endgroup$
0
$\begingroup$

The discriminant of the polynomial $(x-r_1)(x-r_2)\ldots(x-r_n)$ is $\prod_{i<j}(r_i-r_j)^2$. Therefore, if you take $P(x)=x(x-1)(x-i)(x+i)$, its discriminant is

$(0-1)^2(0+i)^2(0-i)^2(1-i)^2(1+i)^2(i+i)^2=-16.$

On the other hand, $P(x)=(x^2-x)(x^2+1)=x^4-x^3+x^2-x$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.