Question

The sum of a non-negative number & its square is less than 12.What could the number be?

Answer 1

x + x^2 < 12
x^2 + x - 12 < 0
(x+4)(x-3) < 0

So where is the corresponding parabola below the x-axis ??
The intercepts are -4 and 3, so
x+x^2 < 12 is true for -4 < x < 3, that is,
all the numbers between -4 and 3

But you want only non-negative x's , so ...

<b>0 ≤ x < 3</b>

(I included the zero, since it is "non-negative" )

checking:
let x = 2.5
2.5 + 2.5^2 = 8.75 , which is < 12
let x = 6
6 + 6^2 = 42 , which is NOT < 12
let x = 2.99
2.99 + 2.99^2 = 11.9301 , which is < 12

Answer 2

didn't know

Answer 3

Tnx