find the discriminant of (2 + sqrt3)x^2 - (4 - sqrt3)x = 1
How do I solve something like this when it has radicands?
b^2-4ac
b=-(4-sqrt3)
a=(2+sqrt3)
c=-1
b^2=16-8sqrt3+3)
b^2-4ac
15-8sqrt3 -4(2+sqrt3)(-1)
15-8sqrt3 +8+3sqrt3)
23-5sqrt3 = 14.339746
check my math.
I think I got 27 - 4sqrt3
b = -(4-√3) = (-4 + √3)
then b^2 = 16 - 8√3 + 3 = 19 - 8√3
Bob had 15-8√3 for that part
modify his solution.
To find the discriminant of a quadratic equation, you'll first need to rewrite it in the form Ax^2 + Bx + C = 0. In this case, we have (2 + √3)x^2 - (4 - √3)x = 1.
To rewrite it, we need to move all the terms to one side of the equation, so subtracting 1 from both sides gives us:
(2 + √3)x^2 - (4 - √3)x - 1 = 0
Now we can identify our A, B, and C values:
A = 2 + √3
B = -(4 - √3)
C = -1
The discriminant (D) is calculated using the formula: D = B^2 - 4AC. Let's substitute our values into the formula:
D = (-(4 - √3))^2 - 4(2 + √3)(-1)
Next, simplify the expression step by step:
D = (16 - 8√3 + 3) - 4(2 + √3)(-1)
D = 19 - 8√3 + 4(2 + √3)
D = 19 - 8√3 + 8 + 4√3
D = 27 - 4√3
Therefore, the discriminant of the given quadratic equation is 27 - 4√3.