Question 192529
Find the quadratic equation whose roots are:
{{{x = (6+4i)}}} and {{{x = (6-4i)}}}
If these are the roots, then the factors of the equation are:
{{{x-(6+4i)}}} and {{{x-(6-4i)}}}
To find the equation with these factors, multiply the factors.
{{{(x-(6+4i))(x-(6-4i)) = highlight(x^2 -12x +52)}}}
One way you could have checked your answer would have been to solve your equation for x using the quadratic formula. Let's see what would we get:
{{{x^2-12x+40 = 0}}}
Use {{{x = (-b+-sqrt(b^2-4ac))/2a}}} and a = 1, b = -12, and c = 40.
{{{x = (-(-12)+-sqrt((-12)^2-4(1)(40)))/2(1)}}}
{{{x = (12+-sqrt(144-160))/2}}}
{{{x = (12+-sqrt(-16))/2}}} or...
{{{x = 6+2i}}} and {{{x = 6-2i}}} Not quite the same as the given roots.