The sum of a non negative number and its square is less than 12 what could the number be?

Answer 1

Let's suppose the number is x, then we can translate the problem into an equation:

x + x^2 < 12

Rearranging the terms, we get:

x^2 + x - 12 < 0

Now we need to find the values of x that satisfy this inequality. We can solve it by factoring the quadratic expression:

(x + 4)(x - 3) < 0

The sign of this expression depends on the signs of the factors. We need the product to be negative, which means that either (x + 4) is negative and (x - 3) is positive, or vice versa:

x + 4 < 0 and x - 3 > 0

or

x + 4 > 0 and x - 3 < 0

Solving these inequalities gives us:

-4 < x < 3

or

x < -4 or x > 3

Since we are looking for non-negative values of x, the solution is:

0 <= x < 3

Therefore, the number x could be any non-negative number less than 3 that satisfies the original equation x + x^2 < 12.

Answer 2

huh?
(x + 4)(x - 3) < 0
this expression is negative only for (-4 < x < 3)