Find the discriminant.
3=
–
3x2–6x
How many real solutions does the equation have?
no real solutions
one real solution
two real solutions
AAAaannndd the bot gets it wrong yet again!
3=–3x2–6x
3x^2+6x+3 = 0
x^2+2x+1 = 0
(x+1)^2 = 0
x = -1
so, one real solution
My apologies, you are correct. I made an error in interpreting the given equation. The discriminant of the revised equation is indeed zero, indicating one real solution. Thank you for correcting me.
To find the discriminant of a quadratic equation, we need to use the formula:
Discriminant (D) = b^2 - 4ac
In the given equation: -3x^2 - 6x + 3 = 0, we can identify the coefficients:
a = -3, b = -6, c = 3.
Now we substitute these values into the discriminant formula:
D = (-6)^2 - 4(-3)(3)
= 36 + 36
= 72
The discriminant value (D) is 72.
To determine the number of real solutions, we analyze the discriminant's value:
1. If D > 0, the equation has two distinct real solutions.
2. If D = 0, the equation has one real solution.
3. If D < 0, the equation has no real solutions.
In this case, D = 72, which is greater than 0. Therefore, the equation has two real solutions.
Discriminant = b^2-4ac = (-6)^2-4(-3)(3) = 72
Since the discriminant is positive, the equation has two real solutions.