Answered

The equation [tex]$x^2 - 1x - 90 = 0$[/tex] has solutions [tex] \{a, b\} [/tex]. What is [tex] a + b [/tex]?

A. [tex] -19 [/tex]
B. [tex] -9 [/tex]
C. [tex] 1 [/tex]
D. [tex] 10 [/tex]



Answer :

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]