The quadratic equation is never smaller than zero, so the inequality has no solutions.
The correct option is never.
When is the inequality true?
Here we have the following inequality:
3x^2 + 4x < - 5
To see when it is true, we need to isolate x.
We can rewrite the inequality as:
3x^2 + 4x + 5 < 0
So the inequality is true when the quadratic equation is smaller than zero.
But notice that it is a quadratic equation with a positive leading coefficient, so it opens upwards.
And the vertex is at:
x = -4/2*3 = -2/3
Evaluating the quadratic there we get:
3*(-2/3)^2 + 4*(-2/3) + 5 = 3.66
So the vertex has a positive y-value, this means that the quadratic equation is never negative, and thus, the inequality has no solutions.
Learn more about quadratic equations:
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