B

Identify the real number \(x\) which converts the numbers \(a_{1} = x\), \(a_{2} = x + 5\) and \(a_{3} = 4x\) into three consecutive numbers of a geometric series.

Identify the real number \(x\) which converts the numbers \(a_{1} = x^{2} - 110\), \(a_{2} = x^{2}\) and \(a_{3} = x^{2} - 1\: 100\) into three consecutive numbers of a geometric series.

Identify the real number \(x\) which converts the numbers \(a_{1} =\log x\), \(a_{2} = 2 +\log x\) and \(a_{3} = 4\log x\) into three consecutive numbers of a geometric series.

Find the values of the real coefficients \(a\), \(b\) and \(c\) such that the quadratic equation \[ ax^{2} + bx + c = 0 \] has solution \(x_{1, 2} =\pm \mathrm{i}\frac{\sqrt{5}} {3} \).