3x^4+27x^2+1200=0

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x = 5, -5, 4i, -4i   ;

Step-by-step explanation:

assume

Now the above equation is a quadratic equation.

There are two solutions of any quadratic equation. Solution of a quadratic equation is given by:

similarly there are two solutions of the quadratic equation which are:

Since

Therefore

; where (the numbers with 'i' are called imaginary numbers)

Therefore

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c