roots

Polynomial Roots

Usage

roots(p)

• It returns the roots of the following polynomial:

• p is a vector containing the coefficents, where p(1) and p(end) correspond to the highest and zeroth order terms, respectively.
• That means p(1) is $p_1$​ and p(end) is $p_{n+1}$​ in Equation (1) above.
• For a $n$-th order polynomial, p should have $n+1$ elements.
• p should be non-empty and should not contain inf nor nan.

Examples

• Roots of the polynomial $0.5x^6+0.5x^5+x^4+2x^3+3x^2+7x+8$. Complex roots are shown in conjugate pairs.

Input

roots([0.5 0.5 1 2 3 7 8])

Output

ans =
  1.138 + 1.345i
  1.138 - 1.345i
 -0.335 + 1.605i
 -0.335 - 1.605i
 -1.303 + 0.469i
 -1.303 - 0.469i

• Polynomial coefficients can be complex. In this case, the roots are not necessarily conjugate pairs.

Input

roots([0 0 1+i 2 3+0.5i])

Output

ans =
 -0.223 + 1.852i
 -0.777 - 0.852i