6. Polynomials a) Generate the elements of the field GF(24) using the irreducible polynomial f(x)= x²+ x³+1 b)(6pt) Using the above results, calculate (x3+x2+1)* (x²+1) c) (6pt) Calculate (-x²+x)-1 d)(6pt) Calculate (x+1)/(x³-1)
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- Explain the following function • hypot( ) • pow( ) • abs( )Quadratic Root Solver For a general quadratic equation y = ax? + bx + c, the roots can be classified into three categories depending upon the value of the discriminant which is given by b2 - 4ac First, if the discriminant is equal to 0, there is only one real root. Then, if the discriminant is a positive value, there are two roots which are real and unequal. The roots can be computed as follows: -b+ Vb? – 4ac 2a Further, if the discriminant is a negative value, then there are two imaginary roots. In this case, the roots are given by b ь? - 4ас 2a 2a Programming tasks: A text file, coeff.txt has the following information: coeff.txt 3 4 4 4 1 4 Each line represents the values of a, b and c, for a quadratic equation. Write a program that read these coefficient values, calculate the roots of each quadratic equation, and display the results. Your program should perform the following tasks: • Check if the file is successfully opened before reading • Use loop to read the file from main…(206)8 = (?)H
- HW3_3 Using built-in functions a) Use the built-in function roots to find all the roots of the polynomial g(x) = x¹+65x³ + 86x + 128. Print your results. b) Given f(x) = x³ – 5x + 10 and g(x) = 4 sin(3x) + 6 Graph these two functions (using different colors for the lines) such that all intersection points are shown. Solve for the intersection points and plot them on the graph with red stars. Use the built-in function brentq. Note: Import appropriate libraries.please help me to solve this simple operation of paython 5. a=77, b=’a’ord('b'): ord(b): chr(a)Question Number Four: Answer each one of the following questions in the space assigned: 1- Simplify each of the following expressions using boolean algebra identities: [4 Marks] a- AB + A( CD + CD') b- ( BC' + A'D) ( AB' + CD') 2- Optimize (simplify) the following boolean function F together with the don't care conditions d in Product-of-sums using k-map: F(A,B.C.D) = IIM (1,3,4,6,9,11)+Ed (0,2,5,8,10,12,14)