Răspuns:
Explicație pas cu pas:
x² - 7x - 6 = 0
a = 1 ; b = - 7 ; c = - 6
∆ = b² - 4ac = (- 7)² - 4 × 1 × (- 6)
∆ = 49 + 24 = 73 > 0 → ∃ x1 , x2 ∈ ℝ ; x1 ≠ x2
[tex]\bf{ x_1 = \frac{ - b + \sqrt{ \triangle} }{2a} = \frac{7 + \sqrt{73} }{2} } \\ [/tex]
[tex]\bf{x_2 = \frac{ - b - \sqrt{ \triangle} }{2a} = \frac{7 - \sqrt{73} }{2} } \\ [/tex]
[tex] \bf{x_1 \times x_2 = \frac{7 + \sqrt{73} }{2} } \times \frac{7 - \sqrt{73} }{2} = \frac{(7 + \sqrt{73})(7 - \sqrt{73} ) }{4} = \frac{49 - 73}{4} = \frac{-24}{4} = \boxed{ \bf{ - 6}}\\ [/tex]
