Question

Срочно нужно решение пожалуйста

Answer 1

По теореме Виета :

${ax}^{2} + bx + c = 0 \\ x_{1} + x _{2} = - \frac{b}{a} \\ x_{1} \times x _{2} = \frac{c}{a}$

2)

1)

${x}^{2} + 11x -8 = 0 \\ x_{1} + x _{2} = - 11 \\ x_{1} \times x _{2} = - 8$

2)

$3 {x}^{2} + 14x - 10 = 0 \\ x_{1} + x _{2} = - \frac{14}{3} = - 4 \frac{2}{3} \\ x_{1} \times x _{2} = - \frac{10}{3} = - 3 \frac{1}{3}$

3)

$x_{1} + x _{2} = 12\\ x_{1} \times x _{2} = 24 \\ {x}^{2} - 12x + 24 = 0$

4)

${x}^{2} + bx - 36 = 0 \\ x_{1} = 4 \\ {4}^{2} + 4b - 36 = 0 \\ 16 - 36 + 4b = 0 \\ - 20 + 4b = 0 \\ 4b = 20 \\ b = 20 \div4 \\ b = 5 \\ \\ {x}^{2} + 5x - 36 = 0 \\ x_{1} + x _{2} = - 5\\ x_{1} \times x _{2} = - 36 \\ x_{1} = 4 \\ x _{2} = - 9$

5)

${x}^{2} + 16x + 7 = 0 \\ x_{1} + x _{2} = - 16 \\ x_{1} \times x _{2} = 7 \\ \\ (x_{1} - x_{2}) {}^{2} = (x_{1} + x_{2}) {}^{2} - 4x_{1}x_{2} = \\ ( - 16) {}^{2} - 4 \times 7 = 256 - 28 = 228$