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1. An interesting method for solving quadratic equations came from India.
The steps are: (a) Move the constant term to the right side of the equation (b) Multiply each term in the equation by four times the coefficient of the x2 term (c) Square the coefficient of the original x term and add it to both sides of the equation (d) Take the square root of both sides (e) Set the left side of the equation equal to the positive square root of the number on the right side and solve for x (f) Set the left side of the equation equal to the negative square root of the number on the right side of the equation and solve for x
Example: Solve x2 + 3x - 10 = 0
x2 + 3x = 10
4x2 +12x = 40
4x2 + 12x + 9 = 40 + 9
4x2 + 12x + 9 = 49
2x + 3 = ±7
2x + 3 = 7 2x + 3 = 7
2x = 4 2x = -10
x = 2 x = -5
Try these:
(a) x2 - 2x - 13 =0
(b) 4x2 - 4x + 3 = 0
(c) x2 + 12x - 64 = 0
(d) 2x2 - 3x - 5 = 0
2. Mathematicians have been searching for a formula that yields prime numbers. One such formula was x2- x + 41. Select some numbers for x, substitute them in the formula, and see if prime numbers occur. Try to find a number for x that when substituted in the formula yields a composite number.
Remaking the quadratic function.
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A laptop computer is purchased for $1500. Its value each year is about 80% of its value in the preceding year. Its value in dollars after t years is given by the exponential function
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They'll need to follow a path to get to the picnic spot. A map of the path is based on a scale of 1:30,000, in cm. If the path is 12 cm on the map how many kilometers is the actual path?
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