Question 192279
Solve for b:
{{{b^4+13b^2+36 = 0}}} Rewrite this as a quadratic equation:
{{{(b^2)^2+13(b^2) + 36 = 0}}} Factor:
{{{(b^2+4)(b^2+9) = 0}}} Apply the zero product rule:
{{{b^2+4 = 0}}} or {{{b^2+9 = 0}}} so...
{{{b^2 = -4}}} or {{{b^2 = -9}}}
{{{b^2 = -4}}} Take the square root of both sides.
{{{b = sqrt(-4)}}} or {{{b = -sqrt(-4)}}} these can be written as:
{{{b = 2i}}} or {{{b = -2i}}} where {{{i = sqrt(-1)}}}
{{{b^2 = -9}}} Take the square root of both sides.
{{{b = sqrt(-9)}}} or {{{b = -sqrt(-9)}}} these can be written as:
{{{b = 3i}}} or {{{b = -3i}}}
The roots are:
{{{b = 2i}}}
{{{b = -2i}}}
{{{b = 3i}}}
{{{b = -3i}}}