Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:(i) `2x^3+x^2-5x+2;``1/2,1,-2` (ii) `x^3-4x^2+5x-2;` `2,\ 1,\ 1`

Explanation

To verify that the given numbers are zeroes of the cubic polynomials and to check the relationship between the zeroes and the coefficients, we will follow these steps:

### Part (i): Polynomial \(2x^3 + x^2 - 5x + 2\) with zeroes \( \frac{1}{2}, 1, -2 \)

**Step 1: Verify \(x = \frac{1}{2}\) is a zero.**

Substituting \(x = \frac{1}{2}\) into the polynomial:

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