Explanation:
To find the zeros of the quadratic function f(x) = 2x² - 10x - 3, we need to solve for x when f(x) is equal to zero. The zeros are the values of x that make the function equal to zero.
So, we set f(x) = 0 and solve for x:
2x² - 10x - 3 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 2, b = -10, and c = -3.
Now, let's plug in the values:
x = (-( -10) ± √((-10)² - 4 * 2 * (-3))) / 2 * 2
x = (10 ± √(100 + 24)) / 4
x = (10 ± √124) / 4
Now, we need to simplify √124:
√124 = √(4 * 31) = 2√31
So, the solutions for x are:
x = (10 + 2√31) / 4
and
x = (10 - 2√31) / 4
Now, we can further simplify these solutions:
x = 5 + √31
and
x = 5 - √31
So, the zeros of the quadratic function f(x) = 2x² - 10x - 3 are x = 5 + √31 and x = 5 - √31.