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how to use barcode in c#.net WorkedOut Solutions to Exercises: s 21 to 29 in Software
692 WorkedOut Solutions to Exercises: s 21 to 29 Quick Response Code Maker In None Using Barcode drawer for Software Control to generate, create Quick Response Code image in Software applications. Decoding QR In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Because d = 0, we know that the quadratic we get by setting the trinomial equal to 0 has one real root with multiplicity 2 That means the original cubic has one more real root besides x = 5, and that root has multiplicity 2 To find it, we can use the quadratic formula with the coefficients and constant named according to the above scheme: x = [ b2 (b22 4a2c)1/2] / (2a2) Because the discriminant is equal to 0, we can simplify this to x = b2 / (2a2) Substituting in the values a2 = 9 and b2 = 24, we get x = ( 24) / [2 ( 9)] = 24/( 18) = 24/18 = 4/3 The roots of the cubic are therefore x = 5 or x = 4/3 The root x = 4/3 occurs with multiplicity 2 The solution set is X = {5, 4/3} 10 The new cubic, written in binomialtrinomial form, looks like this: (x + 3/2)(6x 2 4x + 2) = 0 Let s examine the discriminant d of the trinomial Setting a2 = 6, b2 = 4, and c = 2, we get d = b22 4a2c = ( 4)2 4 6 2 = 16 48 = 32 Because d < 0, the new cubic has only one real root, x = 3/2, exactly as the original cubic did (The two complex roots, however, differ in this equation compared with those in the final challenge in the chapter text For extra credit, you can verify this fact) Make QR In Visual C#.NET Using Barcode creation for .NET framework Control to generate, create QR Code image in .NET applications. QR Code 2d Barcode Generator In .NET Framework Using Barcode creation for ASP.NET Control to generate, create QR image in ASP.NET applications. 26
Denso QR Bar Code Maker In .NET Using Barcode maker for Visual Studio .NET Control to generate, create QR Code image in VS .NET applications. Print QR Code 2d Barcode In VB.NET Using Barcode creation for .NET framework Control to generate, create QR Code JIS X 0510 image in .NET applications. 1 In each of these situations, the trinomial can be factored into the square of a binomial Then that squared binomial is raised to the indicated power (a) Here is the original equation: (x 2 + 6x + 9)2 = 0 UCC.EAN  128 Generation In None Using Barcode encoder for Software Control to generate, create GS1128 image in Software applications. Paint European Article Number 13 In None Using Barcode printer for Software Control to generate, create UPC  13 image in Software applications. 26
Creating Code 128 Code Set B In None Using Barcode generator for Software Control to generate, create ANSI/AIM Code 128 image in Software applications. Generate Barcode In None Using Barcode generation for Software Control to generate, create barcode image in Software applications. In the trinomial, the coefficient of x 2 is 1, the coefficient of x is 6, and the standalone constant is 9 We must find a number, such that adding it to itself yields 6 while squaring it yields 9 That number is 3 The binomial is therefore (x + 3), and we have [(x + 3)2]2 = 0 which simplifies to (x + 3)4 = 0 (b) Here is the original equation: (x 2 4x + 4)3 = 0 In the trinomial, the coefficient of x 2 is 1, the coefficient of x is 4, and the constant is 4 We must find a number, such that adding it to itself yields 4 while squaring it yields 4 That number is 2 The binomial is therefore (x 2), and we have [(x 2)2]3 = 0 which simplifies to (x 2)6 = 0 (c) Here is the original equation: (16x 2 24x + 9)4 = 0 This trinomial is the square of (4x 3) Therefore, the original equation is equivalent to [(4x 3)2]4 = 0 which simplifies to (4x 3)8 = 0 2 In each case, we can remove the exponent from the binomial and then set it equal to 0, obtaining a firstdegree equation The real root of the higherdegree equation is equal to the solution of the firstdegree equation The multiplicity of the root is the value of the exponent n to which the binomial is raised Encoding Code39 In None Using Barcode drawer for Software Control to generate, create Code 3 of 9 image in Software applications. Data Matrix Drawer In None Using Barcode printer for Software Control to generate, create Data Matrix ECC200 image in Software applications. 694 WorkedOut Solutions to Exercises: s 21 to 29
Drawing Identcode In None Using Barcode creation for Software Control to generate, create Identcode image in Software applications. Encode GS1 128 In Visual C# Using Barcode creator for .NET framework Control to generate, create EAN128 image in Visual Studio .NET applications. (a) The real root is found by solving x+3=0 That root is x = 3 Because the binomial is raised to the fourth power, this single real root has multiplicity 4 (b) The real root is found by solving x 2=0 That root is x = 2 Because the binomial is raised to the sixth power, this single real root has multiplicity 6 (c) The real root is found by solving 4x 3 = 0 We can add 3 to each side and then divide through by 4, obtaining the root x = 3/4 Because the binomial is raised to the eighth power, this single real root has multiplicity 8 3 In each of these situations, the trinomial can be factored into the product of two different binomials Then that product is raised to the indicated power (a) Here is the original equation: (x 2 3x + 2)2 = 0 In the trinomial, the coefficient of x 2 is 1, the coefficient of x is 3, and the standalone constant is 2 This trinomial factors into the product of (x 1) and (x 2) Therefore, the original equation can be rewritten as [(x 1)(x 2)]2 = 0 which can be further broken down to (x 1)2(x 2)2 = 0 (b) Here is the original equation: ( 3x 2 5x + 2)5 = 0 In the trinomial, the coefficient of x 2 is 3, the coefficient of x is 5, and the constant is 4 This trinomial factors into the product of (x + 2) and ( 3x + 1) Therefore, we can rewrite the original equation as [(x + 2)( 3x + 1)]5 = 0 USS Code 128 Recognizer In VB.NET Using Barcode decoder for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications. Generating GS1  12 In C# Using Barcode creator for Visual Studio .NET Control to generate, create GTIN  12 image in .NET applications. Painting UPC A In Java Using Barcode maker for Java Control to generate, create UPCA image in Java applications. Draw Code39 In Java Using Barcode creator for Eclipse BIRT Control to generate, create Code 39 Full ASCII image in Eclipse BIRT applications. Drawing Code 3/9 In Java Using Barcode printer for Java Control to generate, create ANSI/AIM Code 39 image in Java applications. EAN13 Recognizer In VS .NET Using Barcode scanner for .NET Control to read, scan read, scan image in .NET framework applications. 
