Question

Complex root of x^2+3x+9=0

Answer 1

`\text{Quadratic formula}`

`ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\x_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)`

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`x^2+3x+9=0\\\\a=1;\ b=3;\ c=9\\\\\Delta=3^2-4(1)(9)=9-36=-27\\\\\sqrt\Delta=√(-27)=√((27)(-1))=√(27)\cdot√(-1)=√(9\cdot3)i=\sqrt9\cdot\sqrt3i=3\sqrt3i`

`x_1=(-3-3\sqrt3i)/(2(1))=-(3)/(2)-(3\sqrt3)/(2)i\\\\x_2=(-3+3\sqrt3i)/(2(1))=-(3)/(2)+(3\sqrt3)/(2)i`

`i=√(-1)`