Equations Reducible to Quadratic Equations Exercise 4.2 Solve the following equations: 1. x 4 − 6 x 2 + 8 = 0 Solution: x4 − 6 x2 + 8 = 0 Let y = x 2 and y 2 = x 4 The above equation becomes: y 2 − 6 y + 8 = 0 y2 − 6 y + 8 = 0 y2 − 4 y − 2 y + 8 = 0 y ( y − 4) − 2( y − 4) = 0 ( y − 2)( y − 4) = 0 y − 2 = 0 and y − 4 = 0 y=2 y=4 2 As‚ y = x x2 = 2 x2 = 4 x = ±2 x=± 2 solution set = { 2‚ − 2‚ 2‚ −2} 2. x −2 − 10 = 3 x−1 Solution: x −2 − 10 = 3 x −1 x −2 − 3 x −1 − 10 = 0 Let
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rational expressions‚ equations (linear‚ quadratic‚ radical‚ rational)‚ systems of equations‚ inequalities‚ functions‚ graphs of quadratic and linear equations and inequalities in two variables‚ complex numbers and applications. 2. Learning Outcomes Upon successful completion of this course‚ students will be able to: 1. perform operations involving polynomials and factoring polynomials 2. solve and graph equations and inequalities such as linear‚ absolute value‚ quadratic‚ rational‚ and radicals
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1 Quadratic Equations in One Unknown (I) Review Exercise 1 (p. 1.4) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Let’s Discuss Let’s Discuss (p. 1.23) Angel’s method: Using the quadratic formula‚ Ken’s method: Using the quadratic formula‚ Let’s Discuss (p. 1.30) The solution obtained by using the factor method is the exact value of the root. However‚ the solution obtained
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A polynomial function with degree ’’ is called a linear function. The most general form of linear function is * Quadratic Function: A polynomial function with degree ’2’ is called a Quadratic function. The most general form of Quadratic equation is * Cubic Function: A polynomial function with degree ’3’ is called cubic function. The
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Maxwell’s EquationsMaxwell’s equations represent one of the most elegant and concise ways to state the fundamentals of electricity and magnetism. From them one can develop most of the working relationships in the field. Because of their concise statement‚ they embody a high level of mathematical sophistication and are therefore not generally introduced in an introductory treatment of the subject‚ except perhaps as summary relationships. These basic equations of electricity and magnetism can be used
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The Maxwell equations Introduction:- One of Newton’s great achievements was to show that all of the phenomena of classical mechanics can be deduced as consequences of three basic‚ fundamental laws‚ namely Newton’s laws of motion. It was likewise one of Maxwell’s great achievements to show that all of the phenomena of classical electricity and magnetism – all of the phenomena discovered by Oersted‚ Ampère‚ Henry‚ Faraday and others whose names are commemorated in several electrical
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The Drake Equation * The Drake Equation was created by Frank Drake in 1960. * estimate the number of extraterrestrial civilizations in the Milky Way. * It is used in the field of Search for ExtraTerrestrial Intelligence (SETI). * National Academy of Sciences asked Drake to organize a meeting on detecting extraterrestrial intelligence. Reason drake equation created * Drake equation is closely related to the Fermi paradox * The Drake Equation is: N = R * fp * ne * fl * fi
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|15 | • Display results in a table. Using technology‚ display your results in a discrete graph • Find a quadratic function that shows the relationship between the number of steps and the area Quadratic Formula: y= ax2 + bx+ c [pic] • Plug in the coordinates to the quadratic formula 1) 1= a (1)2 +b (1) – c 2) 3= a(2)2 b(2) +c 3) 6=a(3)2 +b(3) +c 1= a+ b+ c 3=4a+2b+c
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SL Math Internal Assessment: Stellar Numbers 374603 Mr. T. Persaud Due Date: March 07‚ 2011 Part 1: Below is a series of triangle patterned sets of dots. The numbers of dots in each diagram are examples of triangular numbers. Let the variable ‘n’ represent the term number in the sequence. n=1 n=2 n=3 n=4 n=5 1 3 6
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The sum and the product of three numbers are 0 and 30 respectively. The sum of their cubes is a) c) 0 160 b) d) 90 900 11. If v2 = u2 + 2as‚ then the value of ‘u’ is a) c) v2 - 2as b) d) -3- ± v 2 + 2as ± v 2 − 2as 2as – v2 P118 12. The quadratic equation whose
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