Product of real roots of the equation x2+|x|+9=0

Answer 1

To find the product of the real roots of the equation, we need to find the values of x that satisfy the equation x^2 + |x| + 9 = 0.

First, let's consider the case when x is positive.
In this case, |x| = x, so the equation becomes x^2 + x + 9 = 0.
This is a quadratic equation, and we can use the quadratic formula to solve for x:
x = (-1 ± √(1 - 4*1*9)) / 2
x = (-1 ± √(1 - 36)) / 2
x = (-1 ± √(-35)) / 2

Since the solution involves the square root of a negative number, there are no real roots when x is positive.

Now, let's consider the case when x is negative.
In this case, |x| = -x (since the absolute value of a negative number is positive), so the equation becomes x^2 - x + 9 = 0.
Again, we can use the quadratic formula to solve for x:
x = (1 ± √((-1) - 4*1*9)) / 2
x = (1 ± √(1 - 36)) / 2
x = (1 ± √(-35)) / 2

Again, since the solution involves the square root of a negative number, there are no real roots when x is negative.

Therefore, there are no real roots for the equation x^2 + |x| + 9 = 0.

Answer 2

what a lot of work!
Since x^2 ≥ 0 and |x| ≥ 0 and 9 > 0
x^2+|x|+9 cannot ever be zero!

Answer 3

You are correct. I apologize for the mistake. Since x^2, |x|, and 9 are all non-negative, their sum x^2 + |x| + 9 can never be equal to zero. Therefore, there are no real roots for the equation x^2 + |x| + 9 = 0.