To find the solutions to the quadratic equation [tex]\( 0 = x^2 - 10x - 27 \)[/tex], we start by identifying the solutions, which are the roots of the polynomial.
1. Find the roots:
The roots of the quadratic equation [tex]\( x^2 - 10x - 27 = 0 \)[/tex] will be the values of [tex]\( x \)[/tex] that satisfy this equation.
2. Identify the negative solution:
Among the roots, there will be a negative root and a positive root. We note that:
- The negative solution is between -2 and -1.
3. Identify the positive solution:
Similarly, for the positive root, we find that:
- The positive solution is between 12 and 13.
Thus, we can complete the statements:
- The negative solution is between [tex]\(-2\)[/tex] and [tex]\(-1\)[/tex].
- The positive solution is between [tex]\(12\)[/tex] and [tex]\(13\)[/tex].
