Question 240910
Solve:
{{{x^4+10x^2+9 = 0}}} Rewrite this as:
{{{(x^2)^2+10(x^2)+9 = 0}}} Factor.
{{{(x^2+1)(x^2+9) = 0}}} Apply the zero product rule.
{{{x^2+1 = 0}}} or {{{x^2+9 = 0}}} so...
If {{{x^2+1 = 0}}} then {{{x^2 = -1}}} so {{{x = sqrt(-1)}}} or {{{x = -sqrt(-1)}}}
If {{{x^2+9 = 0}}} then {{{x^2 = -9}}} so {{{x = sqrt(-9)}}} or {{{x = -sqrt(-9)}}}
These answers can be written as: (Note: {{{i = sqrt(-1)}}})
{{{x = i}}}
{{{x = -i}}}
{{{x = 3i}}}
{{{x = -3i}}}
You are correct in stating that there are no REAL solutions, the solutions are complex.