Question

Solve x2 + 2x + 9 = 0

A) X=-2 + or - 4i squareroot 2

b) x= -2 + or - 2i squareroot 2

c) x= -1 + or - 4i squareroot 2

d) x = -1 + or - 2i squareroot 2

Answer 1

\[Given: x^2 + 2x + 9 = 0\\ as\ discriminant\ of\ this\ eq\, D= 2^2-4.1.9=4-36=-32<0\\hence\ its\ roots\ are\ imaginary\\use\ quadratic\ formula\\x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\\ here\ a=1,\ b=2,\ c=9\\we\ have\ x=\frac{ -2 \pm \sqrt{2^2-4.1.9} }{ 2.1 }\\x=\frac{ -2 \pm \sqrt{4-36} }{ 2}\\x=\frac{ -2 \pm \sqrt{-32} }{ 2}\\x=\frac{ -2 \pm \sqrt{2.i^2.4.4} }{ 2}\\x=\frac{ -2 \pm i4\sqrt{2} }{ 2 }\\x=-1\pm\ i2\sqrt{2}\]

Answer 2

@Barrelracing option d correct