Question 982868
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I 'll do one exactly like it for you to use as a model to dop yours:

Find the polynomial with leading coefficient -3 that has degree 3 and roots 4 and 5i.

 Since 5i is a root, so is -5i:

   x = 4,     x = 5i,    x = -5i
 x-4 = 0,  x-5i = 0,  x+5i = 0
 
p(x) = -3(x-4)(x-5i)(x+5i)

p(x) = -3(x-4)(x<sup>2</sup>+5ix-5ix-25i<sup>2</sup>

p(x) = -3(x-4)(x<sup>2</sup>-25(-1))

p(x) = -3(x-4)(x<sup>2</sup>+25)

p(x) = -3(x<sup>3</sup>-4x<sup>2</sup>+25x-100)

p(x) = -3x<sup>3</sup>+12x<sup>2</sup>-75x+300

Edwin</pre>