Find a polynomial function of degree 3 with the given numbers as zeros.
-5, sqrt3, -sqrt3
Would this work as a function for this problem? Please help. Thanks!
f(x) =(x-r1) (x-r2) (x-r3)
=(x-(-5)) (x-sqrt3) (x--sqrt3)
(x+5)) (x-sqrt3) (x+sqrt3)
Yes, this works.
You may be expected to expand the terms to the standard polynomial form. Note that the last two factors are of the form (x-a)(x+a) which expands conviently to two terms.
Thanks I will keep that in mind.
Yes, your attempt at finding the polynomial function with the given zeros is correct.
To find a polynomial function of degree 3 with the given zeros, you can use the fact that if a number "r" is a zero of a polynomial, then the corresponding factor will be (x - r).
In this case, the given zeros are -5, sqrt(3), and -sqrt(3). To find the polynomial function, you need to multiply the factors corresponding to each zero.
So, the polynomial function can be written as:
f(x) = (x - (-5)) (x - sqrt(3)) (x - (-sqrt(3))
= (x + 5) (x - sqrt(3)) (x + sqrt(3))
Simplifying further, you get:
f(x) = (x + 5) (x^2 - 3)
Therefore, the polynomial function of degree 3 with the given zeros is:
f(x) = (x + 5) (x^2 - 3)
Please note that the function f(x) = (x + 5) (x - sqrt(3)) (x + sqrt(3)) could also be used as a valid function for this problem, as both expressions are equivalent.