Download Algebra and Trigonometry by Harley Flanders and Justin J. Price (Auth.) PDF

By Harley Flanders and Justin J. Price (Auth.)

Algebra and Trigonometry

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For example ( x + 2/ = 1 x + 2j = 3 has no solution. For if it did, we would be forced to the false conclusion that 1 = 3. A system with no solution is called inconsistent. Remark 2: A system of two equations may really be a single equation in disguise. For example, in the system fox + 6y=\2 \x + 2y= 4, 3. Quadratic Equations 57 the first equation is three times the second. Any attempt to eliminate one unknown from the system will simultaneously eliminate the other, so the result will be 0 = 0.

Polynomials have special names according to degree: Constant polynomial (zero degree):/(x) = a0. Linear polynomial (first degree): f(x) = a0 + axx, αχφ0. Quadratic polynomial (second degree): f{x) = a0 + axx + a2x2, Cubic polynomial (third degree): f(x) = a0 + axx + a2x2 + a3x3, «-th degree a2 φ 0. a3 φ 0. polynomial: f(x) = a0 + axx + Û^* 2 + · · · + # n _ 1 x n ~ 1 + û n ^ n , Remark: We can write

With a little rearrangement of terms, it can be written as (x2 + x 4- 3)7 = 4x3 - 5, which is of the form ay = b. It follows that γ x2 + x + 3 ' We say that we have solved for y in terms of x, or expressed y in terms of x. 3 The relation between Fahrenheit and centigrade temperatures is F = §C + 32. Express C in terms of F. 2. Linear Equations SOLUTION 55 The equation is linear in F and also linear in C. Solve for C: F - 32 = §C, I(F - 32) = C. Answer C = §(F - 32). 4 Solve for JC: - - - = 10. x y SOLUTION Assume xy Φ 0 and multiply both sides by xy: y — x = \0xy9 y = lOxy + x = (lOy + 1)JC, y I0y+ 1 = x.

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