## 15. Exercise Set 6

#### Exercise 6.1: Quadratic Roots Function

Given: three real values, `a`, `b`, and `c`, and the formula for the roots of a quadratic equation

`x1 = b + (b**2-4ac)**0.5/2a` and

`x2 = b - (b**2-4ac)**0.5/2a`;

Compose: a function of `a`, `b`, and `c` that calculates and returns the roots or some flag values if the roots cannot be calculated.

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#### Exercise 6.2: Relaxation Function

Given: a two-dimensional array, `A`, of real values

Compose: a function of `A` that performs one relaxation step, returning the new array whose values at each position [i, j] are the average of the values from `A` of that position and that position's eight nearest neighbors, [i+/-1, j+/-1].

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#### Exercise 6.3: Polynomial Evaluation Program

Given: a two-dimensional array, `C`, of real valued polynomial coefficients, each row of which contains the coefficients of a single polynomial;

Given: for each row of `C`, the index of each coefficient's position is the exponent of x for that term;

Given: a one-dimensional array `X` of real valued polynomial unknowns, with each element corresponding to the unknown for the whole set of polynomials;

Compose: a function of `C` and `X` that evaluates each polynomial with each unknown, and returns the two-dimensional array containing in each row the value of each polynomial for one of the unknowns.

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