The sum of a non negative number and its square is less than 12 what could the number be?
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.
huh?
(x + 4)(x - 3) < 0
this expression is negative only for (-4 < x < 3)