Can you show that #z^4 + 64# can be factorised into two real quadratic factors of the form #z^2 + az + 8# and #z^2 + bz + 8# but cannot be factorised into two real quadratic factors of the form #z^2 + bz + 16# and #z^2 + bz + 4#?
1 Answer
Explanation:
The factors of
are obtained solving
Here
so
The arrangements
are the only to give trinomials with real coefficients.
The answer is
Another way to solve this problem is by grouping coefficients in
or