To solve the quadratic equation x² – 1x + 90 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a), where a, b, and c are the coefficients from the standard form of the equation ax² + bx + c = 0.
In this equation, a = 1, b = -1, and c = 90. We start by calculating the discriminant (b² – 4ac):
Discriminant = (-1)² – 4(1)(90) = 1 – 360 = -359
Since the discriminant is negative, this indicates that the equation has no real solutions. Instead, we have two complex solutions.
Now we can plug the values into the quadratic formula:
x = (1 ± √(-359)) / 2(1)
This simplifies to:
x = (1 ± i√359) / 2
Thus, the two solutions, a and b, are:
a = (1 + i√359) / 2 and b = (1 – i√359) / 2
In conclusion, the solutions to the equation x² – 1x + 90 = 0 are not real numbers but complex numbers, represented as a and b above.