Documents about Characteristic Polynomial

  • 3 Pages

    Section 3.3

    Virginia Tech, MATH 2214

    Excerpt: ... on is important enough throughout the next few sections that we give it a name: De nition: If ay + by + c y = is a second-order homogeneous equation, then we call the polynomial ak + bk + c = the characteristic polynomial of the di erential equation. (Our textbook uses instead of k for the variable in the characteristic polynomial .) e Characteristic Polynomial e characteristic polynomial for a second-order homogeneous equation is simply the equation of a parabola. e number of roots of a parabola must be zero, one, or two, depending on how o en the parabola crosses the x-axis: If the quadratic formula, k= -b b - ac , a is used to nd the roots, the discriminant (b - ac) identi es the number of roots: a positive discriminant means that both roots are real numbers; a negative discriminant means that both roots are complex numbers. When the discriminant is zero, both roots are real, but they're the same. Two (di erent) real roots When the characteristic polynomial has two real roots k ...