# An upper bound for the positive real roots of a polynomial: posubLMQ

### 5.29.5 An upper bound for the positive real roots of a polynomial: posubLMQ

The posubLMQ command uses the Local Max Quadratic (LMQ) Akritas-Strzebonski-Vigklas algorithm to find upper bounds for the positive real roots of polynomials.

- posubLMQ takes one argument:
  P, a polynomial.
- posubLMQ(P) returns a (non-optimal) upper bound for the positive real roots of P.

#### Examples.

- Input:
  posubLMQ(x^3 - 7*x + 7)
  Output:

  4

- Input:
  posubLMQ(x^5 + 2*x^4 - 6*x^3 - 7*x^2 + 7*x + 7)
  Output:

  4

- Input:
  posubLMQ(x^3 - x^2 -2*x + 2)
  Output:

  3