Select the approximate values of x that are solutions to f(x)=0, where f(x)=-3x^2+3x+9
-3x^2+3x+9=0
x^2 - x - 3 = 0
x = (1 ±√13)/2
F(x) = -3x^2 + 3x + 9 = 0
Divide by -3:
x^2 - x - 3 = 0
Use Quadratic Formula and get:
X = 2.30, and -1.30 = Approx. 2, and 3.
To find the approximate values of x that are solutions to f(x) = 0, where f(x) = -3x^2 + 3x + 9, we can use the quadratic formula.
The quadratic formula states that for any quadratic equation ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, our quadratic equation is -3x^2 + 3x + 9 = 0. We can identify the values of a, b, and c as follows:
a = -3
b = 3
c = 9
Now, we can substitute these values into the quadratic formula to find the approximate values of x that satisfy the equation:
x = (-3 ± √(3^2 - 4(-3)(9))) / (2(-3))
Simplifying this equation, we get:
x = (-3 ± √(9 + 108)) / -6
x = (-3 ± √117) / -6
Now, we can split this equation into two separate solutions:
Solution 1: x = (-3 + √117) / -6
Solution 2: x = (-3 - √117) / -6
Evaluating these expressions, we can use a calculator to find the approximate values of x.
Solution 1: x ≈ -1.3723
Solution 2: x ≈ 1.7056
Thus, the approximate values of x that are solutions to f(x) = 0 are approximately -1.3723 and 1.7056.