Question

For what range of x is 3x^2+5x-28 negative​

Answer 1

3x² ± 5x – 28 < 0

If you meant, 3x² + 5x – 28 < 0, then:

(3x – 7)(x + 4) < 0 {This is an inequality}

Thus, there are two possibilities as follows:

(3x – 7) < 0 or (x + 4) < 0

x < 7/3 or x < –4

These values of x can be combined as x < 7/3

And:


(3x – 7) > 0 or (x + 4) > 0

x > 7/3 or x > –4

These values of x can be combined as x > –4

Thus, the range of values of x is {x: –4 < x < 7/3}

OR

3x² – 5x – 28 < 0, then:

(x – 4)(3x + 7) < 0

x < 4 or x < –7/3

These values can be combined as x < 4

And:


(x – 4)(3x + 7) > 0

x > 4 or x > –7/3

These values can be combined as x > –7/3

The range of values become {x : –7/3 < x < 4}