What are the zeros of the quadratic function f(x) = 2x² - 10x - 3?

Solution:

Zeros of a function are the possible x values of the function for which the function is equal to zero.

The given quadratic function is

f(x) = 2x² - 10x - 3

If f(x) = 0

2x² - 10x - 3 = 0

The formula of a quadratic equation ax² + bx + c = 0 is

x = [-b ± √b² - 4ac]/2a

Here a = 2, b = -10 and c = -3

Substituting the values

x = [- (-10) ± √(-10)² - 4 (2) (-3)]/ 2(2)

x = [10 ± √100 + 24]/ 4

By further calculation

x = [10 ± √124]/4

x = [10 ± 2√31]/4

Taking out 2 as common

x = [5 ± √31]/2

x = [5 + √31]/2 and x = [5 - √31]/2

Therefore, the zeros of the quadratic function are x = [5 + √31]/2 and x = [5 - √31]/2.

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What are the zeros of the quadratic function f(x) = 2x² - 10x - 3?

Summary:

The zeros of the quadratic function f(x) = 2x² - 10x - 3 are x = [5 + √31]/2 and x = [5 - √31]/2.