i already know how to do this question but i would like to learn why my method works
for this question i rearranged the equation 2x^2+13x+32
then did b^2 - 4ac = -87
0 > -87
my teacher said its because i have proven the graph does not cross x axis, but i don't ;understand how that proves this equation
x^2 + 6x + 18 > 2 - (1/2)x
2x^2 + 12x + 36 > 4 - x
2x^2 + 13x + 32 > 0
This is a parabola that opens upward.....
The discriminant is
13^2 - 4(2)(32) = -87
Since the discriminant is negative.....we have no real roots....which means that this parabola lies above the x axis for all x's
Since we worked down to a logical conclusion....then it must be that our assumption was true....that is...
x^2 + 6x + 18 > 2 - (1/2)x for all x's !!!
[Your method is completely valid, YEEEEEET....!!!!]