6x^2-42x=0 (уравнение) Учитель очень удивится увидев твоё верное решение 😼
Найду корень уравнения: 6x^2-42x=0
Решение
Подробное решение
Это уравнение видаa*x^2 + b*x + c = 0 x 1 = D − b 2 a x_{1} = \frac{\sqrt{D} - b}{2 a} x 1 = 2 a D − b x 2 = − D − b 2 a x_{2} = \frac{- \sqrt{D} - b}{2 a} x 2 = 2 a − D − b a = 6 a = 6 a = 6 b = − 42 b = -42 b = − 42 c = 0 c = 0 c = 0 D = b^2 - 4 * a * c = (-42)^2 - 4 * (6) * (0) = 1764 x1 = (-b + sqrt(D)) / (2*a) x2 = (-b - sqrt(D)) / (2*a) x 1 = 7 x_{1} = 7 x 1 = 7 Упростить x 2 = 0 x_{2} = 0 x 2 = 0 Упростить
Сумма и произведение корней
[src] ( 0 + 0 ) + 7 \left(0 + 0\right) + 7 ( 0 + 0 ) + 7 1 ⋅ 0 ⋅ 7 1 \cdot 0 \cdot 7 1 ⋅ 0 ⋅ 7
Теорема Виета
перепишем уравнение6 x 2 − 42 x = 0 6 x^{2} - 42 x = 0 6 x 2 − 42 x = 0 a x 2 + b x + c = 0 a x^{2} + b x + c = 0 a x 2 + b x + c = 0 x 2 + b x a + c a = 0 x^{2} + \frac{b x}{a} + \frac{c}{a} = 0 x 2 + a b x + a c = 0 x 2 − 7 x = 0 x^{2} - 7 x = 0 x 2 − 7 x = 0 p x + q + x 2 = 0 p x + q + x^{2} = 0 p x + q + x 2 = 0 p = b a p = \frac{b}{a} p = a b p = − 7 p = -7 p = − 7 q = c a q = \frac{c}{a} q = a c q = 0 q = 0 q = 0 x 1 + x 2 = − p x_{1} + x_{2} = - p x 1 + x 2 = − p x 1 x 2 = q x_{1} x_{2} = q x 1 x 2 = q x 1 + x 2 = 7 x_{1} + x_{2} = 7 x 1 + x 2 = 7 x 1 x 2 = 0 x_{1} x_{2} = 0 x 1 x 2 = 0 