Which are the roots of the quadratic function f(b) = b² - 75? check all that apply. 
b = 5 square root of 3 
b = -5 square root of 3 
b = 3 square root of 5 
b= -3 square root of 5 
b = 25 square root of 3 
b = -25 square root of 3

Solution:

The given quadratic equation is f(b) = b² - 75

If the value of f(b) is 0, then b is the root of the quadratic equation.

When b = 5√3

f(5√3) = (5√3)² - 75

f(5√3) = 75 - 75 = 0

When b = -5√3

f(-5√3) = (-5√3)² - 75

f(-5√3) = 75 - 75 = 0

When b = 3√5

f(3√5) = (3√5)² - 75

f(3√5) = 45 - 75 = -30 ≠ 0

When b = -3√5

f(-3√5) = (-3√5)² - 75

f(-3√5) = 45 - 75 = -30 ≠ 0

When b = 25√3

f(25√3) = (25√3)² - 75

f(25√3) = 1875 - 75 = 1800 ≠ 0

When b = -25√3

f(-25√3) = (-25√3)² - 75

f(-25√3) = 1875 - 75 = 1800 ≠ 0

Here only 5√3 and -5√3 gives f(b) = 0

Therefore, b = 5√3 and b = -5√3 are the roots of the quadratic equation.

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Which are the roots of the quadratic function f(b) = b² - 75? check all that apply.

Summary:

The roots of the quadratic function f(b) = b² - 75 are b = 5√3 and b = -5√3.