graphing calculator to find all the real zeros of the quadratic function.
f(x)=4x^2-6x-2
To find the real zeros of the quadratic function f(x) = 4x^2 - 6x - 2, enter the function into a graphing calculator and plot the graph. The x-intercepts of the graph represent the real zeros of the function.
Alternatively, you can use the quadratic formula to find the real zeros of the function:
The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / 2a
For f(x) = 4x^2 - 6x - 2, a = 4, b = -6, and c = -2
Substitute these values into the quadratic formula:
x = (6 ± √((-6)^2 - 4*4*(-2))) / 2*4
x = (6 ± √(36 + 32)) / 8
x = (6 ± √(68)) / 8
x = (6 ± √68) / 8
Therefore, the real zeros of the function f(x) = 4x^2 - 6x - 2 are x = (6 + √68) / 8 and x = (6 - √68) / 8.
You can simplify the roots further by finding the value of √68, which is approximately 8.2462:
x = (6 + 8.2462) / 8 = 1.2808
x = (6 - 8.2462) / 8 = -0.5308
Therefore, the real zeros of the function f(x) = 4x^2 - 6x - 2 are approximately x = 1.2808 and x = -0.5308.