Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -6x^2 + 4x + 7.
solve
-6x^2 + 4x + 7 = 0
6x^2 -4x - 7 = 0
use the quadratic formula, since it does not factor.
To find the approximate values of x that are solutions to f(x) = 0, we can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Where a, b, and c are the coefficients of the quadratic equation in the standard form ax^2 + bx + c = 0.
In this case, the equation is f(x) = -6x^2 + 4x + 7. By comparing this equation to the standard form, we can see that a = -6, b = 4, and c = 7.
Now we can substitute these values into the quadratic formula to find the approximate values of x:
x = (-4 ± √(4^2 - 4(-6)(7))) / (2(-6))
Simplifying this equation:
x = (-4 ± √(16 + 168)) / (-12)
x = (-4 ± √184) / -12
Now, to find the approximate values of x, we need to evaluate the expression inside the square root:
√184 ≈ 13.56
Substituting this value back into the equation:
x = (-4 ± 13.56) / -12
Now we can calculate the two possible solutions:
x1 = (-4 + 13.56) / -12 ≈ -0.109
x2 = (-4 - 13.56) / -12 ≈ 1.658
Therefore, the approximate values of x that are solutions to f(x) = 0 are x ≈ -0.109 and x ≈ 1.658.