Question

1. Розв’яжіть рівняння:
1)5x^2 − 10 = 0;
2) x^2 + 4x = 0;
3) 3x^2 + 7x + 2 = 0;
4) x^2 − 3x + 1 = 0;
5) x^2 + x + 3 = 0.

Answer 1

1)

$5 {x}^{2} - 10 = 0 \\ \\ 5 {x}^{2} = 10 \\ \\ {x}^{2} = 2 \\ \\ x1 = \sqrt{2} \\ \\ x2 = - \sqrt{2}$

2)

${x}^{2} + 4x = 0 \\ \\ x(x + 4) = 0 \\ \\ x = 0 \\ \\ x + 4 = 0 \\ x = - 4$

3)

$3 {x}^{2} + 7x + 2 = 0 \\ \\ d = 49 - 24 = 25 \\ \\ x1 = \frac{ - 7 + 5}{6} = - \frac{1}{3} \\ \\ x2 = \frac{ - 7 - 5}{6} = - 2$

4)

${x}^{2} - 3x + 1 = 0 \\ \\ d = 9 - 4 = 5 \\ \\ x1 = \frac{3 + \sqrt{5} }{2} \\ \\ x2 = \frac{3 - \sqrt{5} }{2}$

5) корней нет, так как дискрименант отрицательный

${x}^{2} + x + 3 = 0 \\ \\ d = 1 - 12 = - 11 \\ \\ korney \: net$