How do you solve #7+13x - 2x^2>0#?

1 Answer
Jun 12, 2015

Answer:

Solve y = -2x^2 + 13x + 7 > 0 (1) into inequality (1).

Explanation:

First solve f(x) = -(2x^2 - 13x - 7) = 0 (1) , by the new Transforming Method.
Transformed equation f'(x) = x^2 - 13x - 14. Roots have different signs.
Factor of a.c = -14 -> (-1, 14). This sum is 13 = -b. Then, the 2 real roots are: x = -1 and x = 14. Back to equation (1), the 2 real roots are: -1/2 and 7
Next, plot the 2 numbers -1/2 and 7 on the number line. Use the origin as test point. Replace x = 0 into inequality (1). We get 7 > 0. It is true, therefor O is located on the solution set, meaning interval
(-1/2, 7). Graph:

----------------|--1/2=====|0 ===============|7-------------------

NOTE . There is another better method, the European algebraic method-.->"Between the 2 real roots (x-intercepts), f(x) is opposite in sign to a". In this example, the parabola opens downward (a < 0), between (-1/2) and (7), f(x) > 0.
Using this method students don't need to draw neither graph nor number line. By just looking at the sign of (a), the answer comes out in seconds.