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\\\\√(b^2-4ac)=√(-144)=i√(144)=12i\\\\x_1=(-b-√(b^2-4ac))/(2a);\ x_2=(-b+√(b^2-4ac))/(2a)\\\\x_1=(-(-10)-12i)/(2\cdot1)=(10-12i)/(2)=5-6i\\\\x_2=(-(-10)+12i)/(2\cdot1)=(10+12i)/(2)=5+6i\\\\\text{therefore}\\\\x^2-10x+61=(x-(5-6i))(x-(5+6i))\to A.`