If 3 and 5 are roots of the quadratic function f(x) , find f(2)

First we need to determine the function f(x):

We know that:

if x1 and x2 are roots for the function, then ( x-x1) and ( x-x2) are factors of the function:

Then we conclude that ( x-3) and (x -5) are factors of f(x):

==> f(x) = (x-3) ( x-5)

Let us expand the brackets:

==> f( x) = x^2 - 3x - 5x + 15

==> f(x) = x^2 - 8x + 15

Now that we found f(x) we will calculate f(2) by substituting with x= 2:

==> f(2) = 2^2 - 8*2 + 15

==> f(2) = 4 - 16 + 15

**==> f(2) = 3**

Let the quadratic function be f(x) = ax^2 + bx + c

Now the roots of ax^2 + bx + c are 3 and 5.

=> (x -3 )(x -5)

=> x^2 - 8x + 15

f(x) = x^2 - 8x + 15

=> ax^2 + bx + c = x^2 - 8x + 15

To find f(2), substitute x with 2

=> 2^2 - 8*2 + 15

=> 4 - 16 + 15

=> 3

**Therefore the required value of f(2) is 3.**

If f(x) is the quadratic expression whose roots (or zeros) are x1 and x2, then f(x) = (x-x1)(x-2).

Therefore , if 3 and 5 are the roots of the f(x), then f(x) is given by:

f(x) = (x-3)(x-5) = x^2-3x -5x +15.

f(x) = x^2-8x+15.

Therefore f(x) = x^2-8x+15.

Therefore to find f(2) we put x= 2 in f(x) = x^2-8x-15:

f(2) = 2^2-8*2+15 = 3.

Therefore f(2) = 3.