Question

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

Answer 1

The roots of the given quadratic function
`f(b) = b^2-75` is
`5√(3)\quad` and
`-5√(3)\quad`

Explanation:

Given: Quadratic function
`f(b) = b^2-75`

We have to find the roots of the given quadratic function
`f(b) = b^2-75`

Since, roots of the quadratic equation is the points where the value of function is zero.

That is f(x) = 0

Consider the given function
`f(b) = b^2-75`

Put f(b) = 0

`\Rightarrow b^2-75=0`

Simplify , we have,

`\Rightarrow b^2=75`

Taking square root both side, we have,

`\Rightarrow b=√(75)`

Simplify we have,

`\Rightarrow b=\pm 5√(3)\quad`

Thus, The roots of the given quadratic function
`f(b) = b^2-75` is
`5√(3)\quad` and
`-5√(3)\quad`

Answer 2

`f(b)=b^2-75 \\f(b)=0 \\b^2-75=0 \\b^2=75 \\b=\pm√(75)=\pm√(25*3)=\pm5√(3)`