Question

Which of the following is equivalent to the polynomial below? X^2 - 10x + 61

A. (x-(5-6i))(x-(5+6i))
B. (x+(5-6i))(x+(5-6i))
C. (x+(5-6i))(x-(5+6i))
D. (x+(5-6i))(x+(5+6i))

Answer 1

$x^2-10x+61=...\\\\a=1;\ b=-10;\ c=61\\\\b^2-4ac=(-10)^2-4\cdot1\cdot61=100-244=-144\\\\\sqrt{b^2-4ac}=\sqrt{-144}=i\sqrt{144}=12i\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\x_1=\dfrac{-(-10)-12i}{2\cdot1}=\dfrac{10-12i}{2}=5-6i\\\\x_2=\dfrac{-(-10)+12i}{2\cdot1}=\dfrac{10+12i}{2}=5+6i\\\\\text{therefore}\\\\x^2-10x+61=(x-(5-6i))(x-(5+6i))\to A.$