select the approximate values of x that are solutions to f(x)=0, f(x)=-8x^2+2x+4
To find the approximate values of x that are solutions to the equation f(x) = 0, where f(x) = -8x^2 + 2x + 4, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Let's apply this formula to our equation, f(x) = -8x^2 + 2x + 4:
a = -8, b = 2, and c = 4
x = (-2 ± √(2^2 - 4(-8)(4))) / (2(-8))
x = (-2 ± √(4 + 128)) / (-16)
x = (-2 ± √132) / (-16)
Now, we can simplify further:
x = (-2 ± √(4 * 33)) / (-16)
x = (-2 ± 2√33) / (-16)
At this point, we can simplify the expression even more:
x = (1 ± √33) / 8
Therefore, the approximate values of x that are solutions to f(x) = 0 are:
x ≈ (1 + √33) / 8 and x ≈ (1 - √33) / 8