Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros: 4, −5√. Write the function in standard form.

Answer 1

Zeros: 4, -SQRT(5)

To have only rational roots, we need to add the conjugate of -SQRT(5).

By doing this the middle terms cancel out when we FOIL it.

Zeros: 4, -SQRT(5), SQRT(5)

f(x) = (x - 4)*(x - SQRT(5))*(x + SQRT(5))

f(x) = (x - 4)*(x^2 - 5)

f(x) = x^3 - 4x^2 - 5x + 20

f(x) = x^3 - 4x^2 - 5x + 20

Answer 2

Hi Hanna P.,

-5√ is simply not a recognizable mathematical expression! Please check your submissions after posting, and correct whatever doesn't show as you intended!

Did you mean -√5 ? If so, you still have a problem: a factor of (x+√5) in your polynomial won't multiply through to rational coefficients, no how. Now, if it were ±√5, then you would have them combined to (x^2-25), and so on.

So, what did you intend, or are you clear now?

-- Cheers, -- Mr. d.