Solve the equation 2X^2 + 5X + 2 = 0 stating clearly the number of roots

Firstly, we can identify 2X² + 5X + 2 = 0 as a quadratic equation by the fact it is an X² term, an X term and an integer term all within the same equation, and is equal to zero. To solve a quadratic equation we have 3 main methods:
1) Factorisation2) Completing the square3) The Quadratic Formula
Factorisation is usually the quickest method, but is mainly a skill in spotting the common factors, and is complicated by the 2X² coefficient. Completing the square yields the most information about the solutions, but I would not recommend it to students unless they are very confident with algebraic manipulation of equations.
Therefore I would teach the Quadratic Formula to solve this problem. We can see that our quadratic is of the form aX² + bX + c = 0 and therefore we assign our coefficients:
a = 2 , b = 5 , c = 2
Recalling that the quadratic formula is X = - b ± sqr(b² - 4ac) we can then substitute in our coefficients: 2a
X = - 5 ± sqr(5² - 4x2x2) 2x2
X = - 5 ± sqr(25 - 16) 4
X = - 5 ± 3 4
Evaluating first with the ± symbol acting as a plus sign , and then as a minus sign we obtain:
X = -0.5 and X = -2 Two Solutions