Task 2: (1) (ii) The roots of the quadratic equation ax + bx + c =...

 

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Task 2: (1) (ii) The roots of the quadratic equation ax² + bx + c = 0 are given by X= -b± √b²-4ac 2a . Based on the sign of the discriminant D (i.e. D=b²-4ac), it is possible to discern the nature of the roots according to: • D > 0: A pair of non-equal real valued roots. D = 0: A pair of equal real valued roots. D<0: A pair of non-equal complex valued roots. [25 marks] Write a function that uses a, b and c as inputs to characterize ((i.e., non-equal real, equal real or non-equal complex roots) and compute the roots of the quadratic equation. Write an m-file that tells the user if the quadratic equation ax² + bx+c = 0 with input values of a, b and c has 1) Two real roots with opposite signs 2) Two complex roots 3) Plot the curve ax² + bx+c = 0 over sufficient intervals (i.e., from 0.9 times of the smallest root to 1.1 of the largest root.) to illustrate the results obtained in (1) and (2). Coding: Giving comments and brief information about codes [5 marks] Part (i) results [5 Marks] Part (ii) results [15 Marks] Task 2: (1) (ii) The roots of the quadratic equation ax² + bx + c = 0 are given by X= -b± √b²-4ac 2a . Based on the sign of the discriminant D (i.e. D=b²-4ac), it is possible to discern the nature of the roots according to: • D > 0: A pair of non-equal real valued roots. D = 0: A pair of equal real valued roots. D<0: A pair of non-equal complex valued roots. [25 marks] Write a function that uses a, b and c as inputs to characterize ((i.e., non-equal real, equal real or non-equal complex roots) and compute the roots of the quadratic equation. Write an m-file that tells the user if the quadratic equation ax² + bx+c = 0 with input values of a, b and c has 1) Two real roots with opposite signs 2) Two complex roots 3) Plot the curve ax² + bx+c = 0 over sufficient intervals (i.e., from 0.9 times of the smallest root to 1.1 of the largest root.) to illustrate the results obtained in (1) and (2). Coding: Giving comments and brief information about codes [5 marks] Part (i) results [5 Marks] Part (ii) results [15 Marks]

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