حل   في   ℝ معادلة من الدرجة الثانية 

المعادلة تقبل حلين متمايزين                      حيث :

x_2  ;   x_1    

المعادلة تقبل حل مضاعف                          حيث :

x_1 =  x_2

المعادلة لا تقبل حل في  ℝ

x_1 = \frac{- b- \sqrt{\Delta}}{2a} ∉ℝ

x_2 = \frac{- b+ \sqrt{\Delta}}{2a} ∉ ℝ

a = 1 (slider from -5 to 5, step 0.1)
b = 0 (slider from -5 to 5, step 0.1)
c = -4 (slider from -5 to 5, step 0.1)
f(x) = a * x^(2) + b * x + c
A, B = Intersect(f, xAxis)
texte3: "\Delta= b^2- 4ac =" + (LaTeX[b^(2) - 4 * a * c]) + ""
ac: a * c
Δ: b^(2) - 4 * ac
d: (-b - sqrt(Δ)) / (2 * a)
e: (-b + sqrt(Δ)) / (2 * a)
texte7: "" + a + "x² + " + b + "x + " + c + " = 0"
f_1(x) = a * x^(2) + b * x + c
ac_1: a * c
Δ_1: b^(2) - 4 * ac_1
d_1: (-b - sqrt(Δ_1)) / (2 * a)
texte1_1: "x_1 = \frac{- b- \sqrt{\Delta}}{2a} =" + (LaTeX[d_1]) + ""
e_1: (-b + sqrt(Δ_1)) / (2 * a)
texte7_1: "" + a + "x² + " + b + "x + " + c + " = 0"
f_2(x) = a * x^(2) + b * x + c
ac_2: a * c
Δ_2: b^(2) - 4 * ac_2
d_2: (-b - sqrt(Δ_2)) / (2 * a)
e_2: (-b + sqrt(Δ_2)) / (2 * a)
texte2_1: "x_2 = \frac{- b+ \sqrt{\Delta}}{2a} =" + (LaTeX[e_2]) + ""
texte7_2: "" + a + "x² + " + b + "x + " + c + " = 0"
f_3(x) = a * x^(2) + b * x + c
ac_3: a * c
texte7_3: "" + a + "x² + " + b + "x + " + c + " = 0"