Question

Решите по формулам Дискриминанта D= b²- 4ac ; x 1,2 = -b±√D ÷ 2a

1) 5x² - 8x - 4 = 0
2)4x² - 4x - 3 = 0
3)8x² - 6x + 1 = 0
4)5x² - 26x + 5 = 0

Answer 1

1) x1=-2/5; x2=2
2)x1=1/2; x2=3/2
3)x1=1/4; x2=1/2
4)x1=1/5; x2=5

Answer 2

$1.5x {}^{2} - 8x - 4 = 0 \\ d = {b}^{2} - 4 ac = 64 - 4 \times 5 \times ( - 4) = 65 + 80 = 144 \\ \sqrt{d } = \sqrt{144} = 12 \\ x = \frac{b± \sqrt{d} }{2a} = \frac{8±12}{10} = 2 \: \: : - 0.4$

$2.4x {}^{2} - 4x - 3 = 0 \\ d = b{}^{2} - 4ac = 16 - 4 \times 4 \times ( - 3) = 16 + 48 = 64 \\ \sqrt{} d = \sqrt{64} = 8 \\ x = \frac{b± \sqrt{} d}{2a} = \frac{4±8}{8} = 1.5 \: \: : - 0.5$

$3.8x {}^{2} - 6x + 1 = 0 \\ d = b {}^{2} - 4ac = 36 - 4 \times 8 \times 1 = 4 \\ \sqrt{} d = \sqrt{4} = 2 \\ x = \frac{b± \sqrt{d} }{2a} = \frac{6±2}{16} = 0.25 \: \: 0.5:$

$4.d = b {}^{2} - 4ac = 676 - 4 \times 5 \times 5 = 576 \\ \sqrt{} d = \sqrt{576} = 24 \\ x = \frac{b± \sqrt{d} }{2a} = \frac{26±24}{10} = 0.2 \: \: : 5$