Question

Решите через дискриминант а)х^2-6х+5=0
б)-х^2+7х+8=0
в)5х^2-8х+3=0
г)4х^2-4х+1=0
д)2х^2-6х+5=0
е)х^2-6х=4х-25
ж)х^2-6х+5=0
з)2х^2-5х+3=0
и)4х^2-7х+3=0

Answer 1

Объяснение:

а)

${x}^{2} - 6x + 5 = 0 \\ d = (6 {)}^{2} - 4 \times 1 \times 5 = 36 - 20 = 16 \\ \\ x1 = \frac{6 + 4}{2} = \frac{10}{2} = 5 \\ x2 = \frac{6 - 10}{2} = \frac{ - 4}{2} = - 2$

б)

$- {x}^{2} + 7x + 8 = 0 \\ d = (7 {)}^{2} - 4 \times ( - 1) \times 8 = 49 + 32 = 81 \\ \\ x1 = \frac{ - 7 + 9}{ - 2} = \frac{2}{ - 2} = - 1 \\ x2 = \frac{ - 7 - 9}{ - 2} = \frac{ - 16}{ - 2} = 8$

в)

$5 {x}^{2} - 8x + 3 = 0 \\ d = (8 {)}^{2} - 4 \times 5 \times 3 = 64 - 60 = 4 \\ \\ x1 = \frac{8 + 2}{10} = \frac{10}{10} = 1 \\ x2 = \frac{8 - 2}{10} = \frac{6}{10} = 0.6$

г)

$4 {x}^{2} - 4x + 1 = 0 \\ d = ( {4)}^{2} - 4 \times 4 \times 1 = 16 - 16 = 0 \\ x = \frac{4 + 0}{8} = \frac{4}{8} = + - 0.25$

д)

$2 {x}^{2} - 6x + 5 = 0 \\ d = (6 {)}^{2} - 4 \times 2 \times 5 = 36 - 40 = - 4$

нет корней

е)