Polynomials

⭐ Important Questions

1. Find zeroes of polynomial x² - 3 and verify relationship between zeroes and coefficients.
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   x² - 3 = (x - √3)(x + √3)\nZeroes: √3, -√3\nSum = 0 = -(-3)/1 ✓\nProduct = -3/1 ✓
2. Divide 2x² + 3x + 1 by x + 2 and verify division algorithm.
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   Quotient = 2x - 1, Remainder = 3\nVerification: (x+2)(2x-1) + 3 = 2x² + 3x + 1 ✓
3. If alpha and beta are zeroes of x² - 5x + 6, find 1alpha + 1beta.
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   alpha + beta = 5, alpha x beta = 6\n1alpha + 1beta = alpha + betaalpha beta = 56