Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -3x2 + 4x + 3.
answers:
{–1.00, 1.33}
{-3, 4}
{–1.33, –1.00}
{–0.54, 1.87}
Please advise
using the quadratic formula,
x = (-4±√52)/-6
To find the approximate values of x that are solutions to the equation f(x) = 0 for the given quadratic function f(x) = -3x^2 + 4x + 3, you can use the quadratic formula.
The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = -3, b = 4, and c = 3. Substituting these values into the quadratic formula, you can calculate the solutions:
x = (-4 ± √(4^2 - 4(-3)(3)))/(2(-3))
Simplifying further:
x = (-4 ± √(16 + 36))/(-6)
x = (-4 ± √52)/(-6)
x = (-4 ± 2√13)/(-6)
Now, we can simplify the solutions:
x1 = (-4 + 2√13)/(-6)
x2 = (-4 - 2√13)/(-6)
To find the approximate values, you can use a calculator to evaluate the expressions:
x1 = (-4 + 2√13)/(-6) ≈ 1.333
x2 = (-4 - 2√13)/(-6) ≈ -1
Therefore, the approximate values of x that are solutions to f(x) = 0 are approximately x ≈ 1.333 and x ≈ -1.
Therefore, the correct answer is {–1.00, 1.33}.