a bentech presentation....
polynomial and its zeroes

a project by:
Benny Varghese
PGT Mathematics
JNV pathanamthitta

a =

b =

c =

Factors >>

ax²+bx+c

c: 9
b: 6
a: 1
w_1: b^(2) - ((4 * a) * c)
f(x) = (a * x^(2)) + (b * x) + c
p = Factor(f)
M_1 = Factors(p)
G: (0, -3)
v_1: y(G)
L_1 = Element(M_1, 1)
q = Element(L_1, 1)
m: q(3)
H: (0, (-m))
u_1: y(H)
o: (3 * a)
E: (o, 0)
w: x(E)
L_2 = If(w_1 ≟ 0, Element[M_1, 1], Element[M_1, 2])
r = Element(L_2, 1)
n: r(3)
F: (n, 0)
o_1: x(F)
h = Expand(f)
text1: "P(x)=" + (LaTeX[h]) + ""
ac: (a * c)
det: b^(2) - (4 * ac)
root1: ((-b) + sqrt(det)) / 2 / a
root2: ((-b) - sqrt(det)) / 2 / a
fact1(x) = x - root1
fact2(x) = x - root2
A, B = Root(h)
inputBox2 = Textfield(a)
inputBox3 = Textfield(b)
inputBox4 = Textfield(c)
e = true
text26: "=(" + (LaTeX[a]) + ")x² +(" + (LaTeX[b]) + ")x+(" + (LaTeX[c]) + ")"
C: (o, 0)
D: (3, 0)
i = Line(G, xAxis)
k = OrthogonalLine(D, i)
l = OrthogonalLine(C, i)
I = Intersect(k, i)
J = Intersect(l, i)
K = Intersect(xAxis, yAxis)
q1, k_1, g_1, i_1, d = Polygon(K, G, I, D)
q2, d_1, i_2, j_1, e_1 = Polygon(D, I, J, E)
g = Max((-root1), (-root2))
j = Min((-root1), (-root2))
s = Segment(E, F)
t = Segment(G, H)
L: (n, (-m))
f_1 = Segment(H, L)
h_1 = Segment(F, L)
u: n - o
L_3 = Sequence(w, o_1)
L_4 = Sequence(u_1, v_1)
v: m - 3
M: (Element[L_3, 1], 0)
N: (Element[L_3, 2], 0)
O: (Element[L_3, 3], 0)
P: (Element[L_3, 4], 0)
Q: (Element[L_3, 5], 0)
R: (Element[L_3, 6], 0)
S: (Element[L_3, 7], 0)
T: (Element[L_3, 8], 0)
U: (Element[L_3, 9], 0)
V: (Element[L_3, 10], 0)
W: (0, Element[L_4, 1])
Z: (0, Element[L_4, 2])
A_1: (0, Element[L_4, 3])
B_1: (0, Element[L_4, 4])
C_1: (0, Element[L_4, 5])
D_1: (0, Element[L_4, 6])
E_1: (0, Element[L_4, 7])
F_1: (0, Element[L_4, 8])
G_1: (0, Element[L_4, 9])
H_1: (0, Element[L_4, 10])
text2: "" + p + ""
l_1 = Line(N, i_1)
m_1 = Line(O, i_1)
n_1 = Line(P, i_1)
p_1 = Line(Q, i_1)
q_1 = Line(I, s)
r_1 = Line(Z, g_1)
I_1 = Intersect(l_1, q_1)
J_1 = Intersect(m_1, q_1)
K_1 = Intersect(n_1, q_1)
N_1 = Intersect(p_1, q_1)
O_1 = Intersect(h_1, q_1)
P_1 = Intersect(r_1, p_1)
Q_1 = Intersect(h_1, r_1)
R_1 = Intersect(r_1, n_1)
S_1 = Intersect(f_1, p_1)
T_1 = Intersect(f_1, n_1)
U_1 = Intersect(f_1, m_1)
V_1 = Intersect(r_1, m_1)
W_1 = Intersect(r_1, l_1)
s_1 = Line(I, t)
Z_1 = Intersect(r_1, s_1)
A_2 = Intersect(f_1, s_1)
B_2 = Intersect(r_1, l)
C_2 = Intersect(f_1, l)
D_2 = Intersect(f_1, l_1)
t_1 = Line(R, h_1)
E_2 = Intersect(i, q_1)
F_2 = Intersect(t_1, i)
G_2 = Intersect(f_1, t_1)
a_1 = Line(S, t_1)
b_1 = Line(T, a_1)
c_1 = Line(U, b_1)
f_2 = Line(V, c_1)
H_2: (Element[L_3, 11], 0)
I_2: (Element[L_3, 12], 0)
J_2: (Element[L_3, 13], 0)
K_2: (Element[L_3, 14], 0)
N_2: (Element[L_3, 15], 0)
O_2: (Element[L_3, 16], 0)
P_2: (Element[L_3, 17], 0)
g_2 = Line(H_2, f_2)
Q_2 = Intersect(a_1, i)
R_2 = Intersect(b_1, i)
S_2 = Intersect(c_1, i)
T_2 = Intersect(f_2, i)
U_2 = Intersect(g_2, i)
V_2 = Intersect(f_1, g_2)
W_2 = Intersect(f_1, f_2)
Z_2 = Intersect(f_1, c_1)
A_3 = Intersect(f_1, b_1)
B_3 = Intersect(f_1, a_1)
h_2 = Line(I_2, h_1)
C_3 = Intersect(i, h_2)
D_3 = Intersect(f_1, h_2)
j_2 = Line(A_1, q_1)
E_3 = Intersect(j_2, k)
F_3 = Intersect(l, j_2)
G_3 = Intersect(l_1, h_1)
H_3 = Intersect(l_1, h_1)
I_3 = Intersect(j_2, l_1)
k_2 = Segment(N, D_2)
l_2 = Segment(O, U_1)
m_2 = Segment(P, T_1)
n_2 = Segment(Q, S_1)
p_2 = Segment(R, G_2)
q_2 = Segment(I, O_1)
r_2 = Segment(Q_1, Z)
s_2 = Segment(I, A_2)
t_2 = Segment(A_1, I_3)
a_2 = Segment(J, C_2)
b_2 = Segment(S, B_3)
c_2 = Segment(T, A_3)
d_2 = Segment(U, Z_2)
e_2 = Segment(V, W_2)
f_3 = Segment(H_2, V_2)
q3, g_3, h_3, i_3, j_3 = Polygon(E, F, O_1, J)
q4, k_3, l_3, m_3, n_3 = Polygon(G, J, C_2, H)
M_2 = Intersect(j_2, l_2)
J_3 = Intersect(m_2, j_2)
K_3 = Intersect(h_1, n_2)
M_3 = Intersect(j_2, h_1)
p_3 = Segment(I_3, M_3)
q_3 = Segment(W_1, P_1)
q5, r_3, s_3, t_3, a_3 = Polygon(J, O_1, L, C_2)
N_3, O_3 = Intersect(b_2, q5)
P_3, Q_3 = Intersect(c_2, q5)
R_3, S_3, T_3, U_3 = Intersect(q5, q4)
V_3 = Intersect(r_2, a_2)
W_3 = Intersect(f_1, m_3)
Z_3 = Intersect(s_2, f_1)