Question

If any one can answer all the questions please answer thus question before 12:15 please answer please I eill give 30 points please

Answer 1

$1) \: {x}^{3} - 1 = 0 \\ zeroes = 3 \\ check \: the \: degree \: of \: the \: polynomial \\ \\ (ii) \: {x}^{2} - 7x - 12 = 0 \\ zeroes = 2$

$3) \: \alpha + \beta = 2 \\ \alpha \beta = 3 \\ quadratic \: polynomial \\ = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ = {x}^{2} - 2x + 3$

$4) \: {x}^{3} - 6 {x}^{2} + 11x - 6 = 0 \\ \\ \alpha + \beta + \gamma = \frac{ - b}{a} = \frac{6}{1} = 6 \ \\ \\ \alpha \beta + \beta \gamma + \gamma \alpha = \frac{c}{a} = \frac{11}{1} = 11 \\ \\ \alpha \beta \gamma = \frac{ - d}{a} = \frac{6}{1}$

$5) \: 3 {x}^{2} + 11x - 4 = 0 \\ \\ 3 {x}^{2} + 12x - x - 4 = 0 \\ \\ 3x(x + 4) - 1(x + 4) = 0 \\ \\ (3x - 1)(x + 4) \\ \\ x = \frac{1}{3} \: or \: x = - 4 \\ \\ let \\ \\ m = \frac{1}{3} \: and \: n = - 4 \\ \\ \frac{m}{n} + \frac{n}{m} = \frac{ - 4}{3} + \frac{ - 12}{1} \\ \\ = - 13.33$

$6) \: coefficient \: of \: {x}^{5} = - 6 \\ degree = 7 \\ constant = - 6 \\ \\ constant = - 6 \\ coefficient = 7$