Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -9x2 + 2x + 6.
a) {-0.71, 0.94}
b) {-9,2}
c) {-0.22, -0.67}
d) {-1.50, 0.33}
You can use the same reasoning as the answer to your previous post.
To find the approximate values of x that are solutions to the equation f(x) = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation f(x) = -9x^2 + 2x + 6, we can identify a = -9, b = 2, and c = 6.
Plugging these values into the quadratic formula, we have:
x = (-2 ± √(2^2 - 4(-9)(6))) / (2(-9))
x = (-2 ± √(4 + 216)) / -18
x = (-2 ± √220) / -18
Now, we can simplify the expression under the square root:
√220 can be approximated as √(169 + 51). Since 169 is a perfect square (13^2), we can simplify further:
√(169 + 51) = √(13^2 + 51)
√(169 + 51) = √(169) * √(1 + 51/169)
√(169 + 51) = 13 * √(220/169)
√(169 + 51) = 13 * √(220)/13
√(169 + 51) ≈ √(220)
Hence, the approximate values of x are:
x ≈ (-2 ± √(220)) / -18
Now, let's evaluate the options provided:
a) {-0.71, 0.94}
b) {-9, 2}
c) {-0.22, -0.67}
d) {-1.50, 0.33}
Comparing the given options with the approximate values, we see that option (c) {-0.22, -0.67} closely matches the calculated values, which are (-2 ± √(220)) / -18. Therefore, the correct answer is:
c) {-0.22, -0.67}