# A lower bound for the positive real roots of a polynomial: poslbdLMQ

### 5.29.6 A lower bound for the positive real roots of a polynomial: poslbdLMQ

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

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

#### Examples.

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

  1
  2

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

  1
  2

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

  1
  2