For the following equation, state the value of the discriminant and then describe the nature of the solutions.
6x^2-3x+2=0
I came up with the value of the discriminant as 35.
Then I came up with it has two real solutions.
Is this correct?
(-3)^2 - 4*6*2
9 - 48
negative
so no real solutions
The only problem is with the way you wrote it out is that according to my choices for the solutions is:
The equation has one real solution.
The equation has two imaginary solutions.
The equation has two real solutions.
It doesn't give me the option for no real solutions :(
Damon said there are no REAL solutions...that would leave your option of the imaginary solutions...
7.7
Yes, your answer is correct!
To find the value of the discriminant, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, a = 6, b = -3, and c = 2. Plugging these values into the formula, we get:
x = (-(-3) ± √((-3)^2 - 4(6)(2))) / (2(6))
= (3 ± √(9 - 48)) / 12
= (3 ± √(-39)) / 12
Since the discriminant, which is located inside the square root, is negative (-39), we know that the equation has no real solutions. Instead, it has two complex solutions.