Solve the eqution
`x^(2)+ixsqrt(3)+18=0`.

Options

A. `2sqrt(2)i` and ` -3sqrt(2)i`.
B. `2sqrt(3)i` and ` -3sqrt(2)i`.
C. `2sqrt(3)i` and ` -2sqrt(3)i`.
D. `2sqrt(3)i` and ` -3sqrt(3)i`.

Answer

D

Explanation

`x^(2)+ixsqrt(3)+18=0`
Here, `a=1, b=isqrt(3), c=18`
Now, from Sridharacharya's formula
`" "x= (-bpmsqrt(b^(2)-4ac))/(2a) `,
`" "x=(-isqrt(3)pmsqrt((isqrt(3))^(2)-4(1)(18)))/(2(1))`
`" "=(-isqrt(3)pmsqrt(3i^(2)-72))/(2)`
`" "=(-isqrt(3)pmsqrt(3i^(2)+72i^(2)) )/(2)`
`" "=(-isqrt(3)pmsqrt(75i^(2)))/(2)=(-isqrt(3)pm5sqrt(3) i)/(2)`
Complex Numbers and Quadratic Equation
`rArr" "x=(-isqrt(3)+5sqrt(3)i)/(2)" or "x=(-isqrt(3)- 5sqrt(3)i)/(2)`
`rArr" "x=2sqrt(3)i" or "x=-3sqrt(3)i`
Therefore, the roots of the given equation are `2sqrt(3)i` and ` -3sqrt(3)i`.