To find the sum of the roots of the quadratic equation \( x^2 - x - 90 = 0 \), we can use Vieta's formulas. Vieta's formulas relate the coefficients of the polynomial to sums and products of its roots.
For a quadratic equation of the form \( ax^2 + bx + c = 0 \), the sum of the roots \( a \) and \( b \) can be found using the formula:
[tex]\[ a + b = -\frac{b}{a} \][/tex]
In the given quadratic equation \( x^2 - x - 90 = 0 \):
- The coefficient \( a \) (the coefficient of \( x^2 \)) is 1.
- The coefficient \( b \) (the coefficient of \( x \)) is -1.
- The constant term \( c \) is -90.
So, according to Vieta's formulas, the sum of the roots is:
[tex]\[ a + b = -\frac{b}{a} = -\frac{-1}{1} = 1 \][/tex]
Thus, the sum of the roots \( a \) and \( b \) is:
[tex]\[ a + b = 1 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
