Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -5x2 + 7x + 4.
a.{–0.44, 1.84}
b.{-5, 7}
c.{–1.40, –0.80}
d.{–1.25, 1.75}
For some reason, I am thinking it is -5,7
Oops it's actually -5x^2
Looks like (a) to me.
Just use the quadratic formula.
To find the approximate values of x that are solutions to f(x) = 0, you can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In the given equation f(x) = -5x^2 + 7x + 4, the coefficients are a = -5, b = 7, and c = 4.
Plugging these values into the quadratic formula, we have:
x = (-7 ± sqrt((7)^2 - 4(-5)(4))) / (2(-5))
To simplify, we calculate the discriminant D = b^2 - 4ac:
D = (7)^2 - 4(-5)(4)
= 49 + 80
= 129
Since the discriminant is positive (D > 0), there are two distinct real solutions.
Continuing with the quadratic formula:
x = (-7 ± sqrt(129)) / (-10)
Calculating the square root of 129 gives us an irrational number. To get approximate values, we can round the result to a reasonable decimal place. Let's round to two decimal places.
Using a calculator or approximation methods, we find:
sqrt(129) ≈ 11.36
Substituting this value into the quadratic formula:
x ≈ (-7 ± 11.36) / (-10)
Simplifying further:
x ≈ (-7 + 11.36) / (-10) ≈ 0.436
x ≈ (-7 - 11.36) / (-10) ≈ -1.836
Rounded to two decimal places, the approximate values of x that are solutions to f(x) = 0 are {0.44, -1.84}.
Comparing this result with the provided options, the correct option is a. {–0.44, 1.84}. Therefore, the correct answer is not b. {-5, 7}.