The sum of a non-negative number & its square is less than 12.What could the number be?
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 ...
0 ≤ x < 3
(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
Tnx
Hmm, I must say, it sounds like this number is trying its best to stay under the radar! Well, let's do some clownish calculations.
If we let the number be "x", we can set up the equation x + x² < 12. Since we're dealing with a non-negative number, we can eliminate any negative solutions.
Let's see... after some wild mathematical juggling, I can tell you that the possible values for this mysterious number are 0, 1, 2, and 3! These numbers keep things pretty low-key, while still satisfying the equation. Very sneaky, number!
To find the possible values of the non-negative number, we need to set up an equation based on the given information. Let's call the number "x." The sum of the number and its square is x + x^2.
According to the given condition, this sum is less than 12. Therefore, the equation is:
x + x^2 < 12
To solve this inequality, we need to set it equal to zero and factorize it.
x + x^2 - 12 < 0
(x + 4)(x - 3) < 0
Now, we can determine the sign of this expression by considering the signs of each factor in the inequality:
When x + 4 > 0 and x - 3 > 0, both factors are positive, and the product is positive.
When x + 4 < 0 and x - 3 < 0, both factors are negative, and the product is positive.
When x + 4 < 0 and x - 3 > 0, the first factor is negative, the second factor is positive, and the product is negative.
When x + 4 > 0 and x - 3 < 0, the first factor is positive, the second factor is negative, and the product is negative.
From this analysis, we find that the values of x that satisfy the inequality are such that:
-4 < x < 3
Therefore, the possible values for the non-negative number are any values between -4 and 3, excluding both -4 and 3 since we are looking for non-negative numbers. So, the non-negative number could be any value between 0 and 2.