Which statement concerning the equation x^2+2=x is true?
Its discriminant is 0 , so it has no solution.
Its discriminant is 0 , so it has one real solution.
Its discriminant is -7, so it has two complex solutions.
Its discriminant is -7, so its solutions are negative.
Well, it seems that this equation is trying to play hide and seek with us. Let's see what the joke is here. The equation is x^2 + 2 = x, and we're talking about discriminants and solutions. Now, I hate to be the bearer of bad news, but the discriminant of this equation is actually 9. So none of the options provided really hit the nail on the head. Looks like this equation is just too shy to reveal its true nature. Perhaps it's a little equation in search of some attention. Keep searching, my friend!
To determine the discriminant of the equation x^2 + 2 = x, we first need to rearrange the equation to make it quadratic in form. Subtracting x from both sides gives us x^2 - x + 2 = 0.
The discriminant (denoted as Δ) of a quadratic equation ax^2 + bx + c = 0 is given by the formula Δ = b^2 - 4ac.
Comparing the equation x^2 - x + 2 = 0 to the form ax^2 + bx + c = 0, we have a = 1, b = -1, and c = 2.
Plugging these values into the discriminant formula, we get Δ = (-1)^2 - 4(1)(2) = 1 - 8 = -7.
Since the discriminant is negative, the equation has two complex solutions.
Therefore, the correct statement is: Its discriminant is -7, so it has two complex solutions.
To determine which statement is true concerning the equation x^2 + 2 = x, we need to analyze the discriminant of the equation. The discriminant can be found using the formula: b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation (in the form ax^2 + bx + c = 0).
In this case, the equation x^2 + 2 = x can be rearranged as x^2 - x + 2 = 0. Comparing this equation to the standard form ax^2 + bx + c = 0, we find that a = 1, b = -1, and c = 2.
Now, let's calculate the discriminant:
b^2 - 4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7.
The discriminant for this equation is -7.
Now, let's evaluate each statement based on the value of the discriminant:
1) "Its discriminant is 0, so it has no solution."
Since the discriminant is -7, this statement is false.
2) "Its discriminant is 0, so it has one real solution."
Again, since the discriminant is -7, this statement is false.
3) "Its discriminant is -7, so it has two complex solutions."
Given that the discriminant is -7, this statement is true. The equation has two complex solutions.
4) "Its discriminant is -7, so its solutions are negative."
The value of the discriminant does not provide any information about whether the solutions are positive or negative, so this statement is false.
Therefore, the correct statement is: "Its discriminant is -7, so it has two complex solutions."
set it up in the usual way
x^2-x+2 = 0
b^2-4ac = 1-8 = -7
so, what does a negative discriminant tell you?