+9466 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.
+9466 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.
