This applet is an addition to the early applet. Here, in addition to calculating the roots of a polynomial equation of degree 5, the points of extrema and inflections are calculated using symbolic formulas.
Case: 1
Case: x0=1; a₁=1; a₂=1; a₃=-4; a₄=-3; a₅=3;
Roots 3: Real- z3, z4, z5 and Complex Conjugate numbers- z1&z2.
Stationary points: 4 (R1,R2,R3,R4). r1, r2, r3, r4 -the roots of the equation f'(x)=0 are real numbers.
Inflection points: 3 ( I1, I2, I3). i1, i2, i3-the roots of the equation f''(x)=0 are real numbers.
Case: 2
Case: x0=-0.5; a₁=1; a₂=1; a₃=5; a₄=-3; a₅=3;
Roots 3: Real- z5 and 2 pairs Complex Conjugate numbers- z1&z2 and z3&z4.
Stationary points - no. The roots of the equation f'(x): r1,r2,r3,r4 are complex numbers.
Inflection points: one - I1. The roots of the equation f''(x): 1 real (i1) and two are complex numbers (i2&i3).
