+0  
 
0
268
1
avatar+644 

For what values of x is -5x^2+17x-12 negative?
 

waffles  Nov 8, 2017

Best Answer 

 #1
avatar+7339 
+1

First let's find the  x  values that make it equal  0 .

 

-5x2 + 17x - 12  =  0          Using the quadratic formula....

 

x  =  [  -17 ± √( 172 - 4(-5)(-12) )  ] / [  2(-5)  ]  =  [  -17 ± 7  ] / [  -10  ]

 

x  =  1     or     x  =  12/5

 

The graph of this expression is a parabola that opens down, so

the  x  values that make it less than  0  will be in the interval

 

(-∞, 1) U (12/5 , ∞)

 

To make sure, let's test points.

 

-5(0)2 + 17(0) - 12  =  -12  <  0

-5(2)2 + 17(2) - 12  =    2   >  0

-5(3)2 + 17(3) - 12  =  -21  <  0

 

Or look at a graph.

hectictar  Nov 8, 2017
edited by hectictar  Nov 20, 2017
 #1
avatar+7339 
+1
Best Answer

First let's find the  x  values that make it equal  0 .

 

-5x2 + 17x - 12  =  0          Using the quadratic formula....

 

x  =  [  -17 ± √( 172 - 4(-5)(-12) )  ] / [  2(-5)  ]  =  [  -17 ± 7  ] / [  -10  ]

 

x  =  1     or     x  =  12/5

 

The graph of this expression is a parabola that opens down, so

the  x  values that make it less than  0  will be in the interval

 

(-∞, 1) U (12/5 , ∞)

 

To make sure, let's test points.

 

-5(0)2 + 17(0) - 12  =  -12  <  0

-5(2)2 + 17(2) - 12  =    2   >  0

-5(3)2 + 17(3) - 12  =  -21  <  0

 

Or look at a graph.

hectictar  Nov 8, 2017
edited by hectictar  Nov 20, 2017

36 Online Users

avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.