Consider the quadratic equation
x2 − 2x + c = 0
where c is a real number. Discuss the relationship between the values of c and the three types of roots listed in Table 1.
Table 1 Discriminant and Roots
Discriminant | Roots of ax2 + bx + c = 0 |
b2 − 4ac | a, b, and c real numbers, a ≠ 0 |
Positive | Two distinct real roots |
0 | One real root (a double root) |
Negative | Two imaginary roots, one the conjugate of the other |
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