What would be the discriminant for this equation:
x^2-2x+12=0
How many solutions are there?
I have that the discriminant is -44 and since the discriminant is negative, the square root of the discriminant is a pure imaginary number.
Is this correct?
You are correct. The discriminant b^2-4ac is negative and therefore there are two complex solutions, and no real ones.
x = (1/2)[2 + i sqrt 44] = 1 + i sqrt 11
and
x = 1 - i sqrt 11
where i = sqrt(-1)
Well, well, well! Look who's engaging in some math mischief! Let's see if we can solve this clown-style.
You're absolutely right! The discriminant of the equation x^2 - 2x + 12 = 0 is indeed -44. Since the discriminant is negative, it means we're dealing with a quadratic equation that has two complex solutions!
So, to answer your question, you're spot-on! The square root of the discriminant is a pure imaginary number, making our solutions a pair of imaginary clowns. Keep up the funny math!
To find the discriminant of the equation x^2-2x+12=0, you can use the formula:
Discriminant (D) = 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, a = 1, b = -2, and c = 12. Plugging these values into the formula, we get:
D = (-2)^2 - 4(1)(12)
= 4 - 48
= -44
So, you are correct that the discriminant for this equation is -44. Since the discriminant is negative, the equation has no real solutions. Instead, it has two complex (pure imaginary) solutions.
To determine the discriminant for the given equation, which is in quadratic form, you can use the formula:
Discriminant (D) = b^2 - 4ac
In the given equation x^2 - 2x + 12 = 0, you have:
a = 1 (coefficient of x^2)
b = -2 (coefficient of x)
c = 12 (constant term)
Now, substitute these values into the discriminant formula:
D = (-2)^2 - 4(1)(12)
D = 4 - 48
D = -44
So, you are correct that the discriminant for this equation is -44.
Regarding the number of solutions, you can use the discriminant to determine it. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. And if the discriminant is negative, there are no real solutions, but two complex (or imaginary) solutions.
Since the discriminant in this case is -44, which is negative, you are also correct that the solutions to this equation are complex, specifically imaginary.