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

thanks

YEEEEEET Apr 19, 2019

#1**+2 **

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....!!!!]

CPhill Apr 19, 2019