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

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

Nov 8, 2017

#1
+7599
+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.

Nov 8, 2017
edited by hectictar  Nov 20, 2017

#1
+7599
+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