SOLUTION: The inequality 0<2x^2+bx+5 has an infinite number of real solutions when..
1) -2√10 < b < 2√10
2) b<-2√10 or b> 2√10
3) -2√10 ≤ b ≤ 2&
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Question 1098764: The inequality 0<2x^2+bx+5 has an infinite number of real solutions when..
1) -2√10 < b < 2√10
2) b<-2√10 or b> 2√10
3) -2√10 ≤ b ≤ 2√10
4) b≤ -2√10 or b≤ 2√10
Would it work if I used the discriminant formula to solve this? And how would I solve it? I would greatly appreciate an answer!
Answer by josgarithmetic(39631) (Show Source): You can put this solution on YOUR website!
The quadratic function would be greater than zero for all x. This means the discriminant must be negative. That should help you.
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Discriminant is ,
.
The function is a parabola having a minimum vertex and the parabola opens upward. If , then the parabola will cross the x-axis in two places and there will be some points below the x-axis. If , then the parabola will not touch nor cross the x-axis anywhere, and all points of the parabola will be greater than 0 (or all points will be above the x-axis).
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