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avatar+844 

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

 Apr 19, 2019
 #1
avatar+106539 
+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....!!!!]

 

 

cool cool cool

 Apr 19, 2019
 #2
avatar+844 
0

thank you

YEEEEEET  Apr 19, 2019

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