Algebra
Answer the ff:
a. Evaluate the sum and product of the roots of 3x2 + 7x – 5 = 0.
b. What is the equation whose roots are reciprocal of the roots of the equation of 2x2 + 5x + 2 = 0?
c. Which of the following is a lower bound of 2x3 - 5x2 - 8x + 11 = 0?
d. An arithmetic progression starts with 3, has 9 terms, and the middle term is 19. Determine the sum of the first 9 terms.
e. Suppose that the measurement of time during the day is converted to the metric system so that each day has 10 metric hours, and each metric hour has 100 metric minutes. Digital clocks would then be produced that would read 9:99 just before midnight, 0:00 at midnight, 1:25 at the former 3:00 AM, and 7:50 at the former 6:00 PM. After the conversion, a person who wanted to wake up at the equivalent of the former 6:36 AM would set his new digital alarm clock for A:BC, where A, B, and C are digits. Find 100A + 10B + C.
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