Question

Cho phương trình \(a{x^2} + bx + c = 0(a \ne 0)\) có hai nghiệm \({x_1},{x_2}\).

Tính \({x_1} + {x_2}\) và \({x_1}.{x_2}\).

Answer 1

\({x_1} + {x_2}\) = \(\frac{{ - b + \sqrt \Delta  }}{{2a}} + \frac{{ - b - \sqrt \Delta  }}{{2a}} =  - \frac{{2b}}{{2a}} =  - \frac{b}{a}\)

\({x_1}.{x_2} = \frac{{ - b + \sqrt \Delta  }}{{2a}}.\frac{{ - b - \sqrt \Delta  }}{{2a}} = \frac{{{{( - b)}^2} - \Delta }}{{4{a^2}}} \\= \frac{{{b^2} - ({b^2} - 4ac)}}{{4{a^2}}} = \frac{{4ac}}{{4{a^2}}} = \frac{c}{a}\)