Select the approximate values of x that are solutions to f(x) = 0, where f(x) =- 8x2+5x+3.
I don't know if i did it correctly but my answer is (1.00,-0.38
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f(x) is a quadratic equation for which exact solutions may be obtained in many ways, including factoring, completing the square, and quadratic formula.
Are you studying numerical methods where an approximate solution is required instead of an exact one?
Yes, your answer is correct...to two decimal places. Usually multiple solutions are enclosed in braces to indicate that each number is part of a set of solutions, like {1, -3/8}.
(1.00, -0.38) would be an ordered pair.
To find the approximate values of x that are solutions to f(x) = 0 for the given quadratic function f(x) = -8x^2 + 5x + 3, we can use the quadratic formula or graphical methods.
1. Quadratic Formula:
The quadratic formula is used to find the solutions to a quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are coefficients. For our function f(x) = -8x^2 + 5x + 3, a = -8, b = 5, and c = 3.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/(2a)
Applying this formula to our function, we have:
x = (-5 ± √(5^2 - 4 * -8 * 3))/(2 * -8)
x = (-5 ± √(25 + 96))/( -16)
x = (-5 ± √(121))/( -16)
x = (-5 ± 11)/-16
Therefore, the approximate solutions for x are:
x = (-5 + 11)/-16 = 6/-16 = -0.375 (approximately -0.38)
x = (-5 - 11)/-16 = -16/-16 = 1
So the approximate values of x that are solutions to f(x) = 0 are x = -0.38 and x = 1.
2. Graphical Method:
Another way to approximate the solutions to a quadratic equation is by graphing the function and finding the x-intercepts. In this case, we plot the function f(x) = -8x^2 + 5x + 3 on a graphing calculator or software.
The x-intercepts represent the points where the function intersects the x-axis, meaning f(x) = 0. By observing the graph, we can estimate the approximate x-values of the x-intercepts.
In this case, we can see that there are two x-intercepts, one at approximately x = -0.38 and the other at x = 1.
Both methods provide the same approximate solutions: x = -0.38 and x = 1.