Bonjour,
1)
[tex]ax^2+bx+c=0\ avec\ a\neq0\ ,\ \Delta=b^2-4ac > 0\ et\ a,b,c\in\mathbb{R}\\\quad \\0=ax^2+bx+c\\\quad =a[x^2+\dfrac{b}{a}x+\dfrac{c}{a}]\\\quad =a[x^2+2\dfrac{b}{2a}x+\dfrac{b^2}{4a^2}-\dfrac{b^2}{4a^2}+\dfrac{c}{a}]\\\quad =a[x^2+2\dfrac{b}{2a}x+\dfrac{b^2}{4a^2}-\dfrac{b^2}{4a^2}+\dfrac{c}{a}]\\\quad =a[(x+\dfrac{b}{2a})^2-(\dfrac{b^2-4ac}{4a^2})]\\\quad =a[(x+\dfrac{b}{2a}-\dfrac{\sqrt{b^2-4ac}}{2a})(x+\dfrac{b}{2a}+\dfrac{\sqrt{b^2-4ac}}{2a})]\\\quad \\\quad =a(x-x_1)(x-x_2)\\[/tex]
[tex]\boxed{x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}}\\\quad \\\quad \\\boxed{x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\}\quad \\\quad \\\quad \\\quad \\\boxed{x_1+x_2=-\dfrac{b}{a}}\\\quad \\\quad \\\boxed{x_1*x_2=\dfrac{c}{a}\\}[/tex]
