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Quadratic Equations

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For Project 1, complete all 6 steps (a-f) as shown in the example. For Project 2, please select at least 5 numbers; 0 (zero), 2 even and 2 odd. Make sure you organize your paper into separate projects.

Project 1:

An interesting method for solving quadric 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 term x2.
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 to the right 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.
try these:
a. x2 - 2 x- 13 =0
b. 4x2 -4 x + 3=0
c. x2 +12x- 64=0
d. 2 x2 - 3x-5+0

Project 2:

Mathematicians have been searching for a formula the yields prime numbers. One such formula was x2-x+41. Select some numbers for x, substitute then in the formula, and see if the prime numbers occur. Try to find a number for x that when substituted in the formula yields a composite number.

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This solution is comprised of detailed step-by-step calculations and explanation of the given problems and provides students with a clear perspective of the underlying concepts.

Solution provided by:
Anwesha Ghosh, MSc
Education
  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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