Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. 2, 3, 5√

Answer 1

Your given zeros are 2, 3, and √5 (I'm assuming you intended the 5 to be under the radical).

The need for rational coefficients indicates that you must have a way to get rid of the radical in one of your zeros. To do this, you must also have a zero of -√5.

Write your zeros as x= equations

x = 2 x = 3 x = √5 x = -√5 Set the equations equal to zero

x - 2 = 0 x - 3 = 0 x - √5 = 0 x + √5 = 0 Use ( ) and multiply your factors. Set = to f(x)

f(x) = (x - 2)(x - 3)(x - √5)(x + √5) Multiply your first two factors and your last 2 factors

f(x) = (x² - 5x + 10)(x² - 5) Multiply them together

f(x) = x⁴ - 5x³ + 5x² +25x - 50