Question

Find a cubic function with the given zeros. square root of 5, - square root of 5, 7

Answer 1

To find a cubic function with the given zeros, we need to use factoring. The factored form of a cubic function with zeros a, b, and c is (x-a)(x-b)(x-c). Substituting the given zeros, we get (x-√5)(x+√5)(x-7).

Step-by-step explanation:

To find a cubic function with the given zeros, we need to use the concept of factoring. The zeros of a cubic function are the values of x when the function equals zero. So, the given zeros are √5, -√5, and 7. To create the cubic function, we need to use the factored form. The factored form of a cubic function with zeros a, b, and c is given by: f(x) = (x-a)(x-b)(x-c).

Substituting the given zeros into the factored form, we have: f(x) = (x-√5)(x-(-√5))(x-7).

Simplifying further, we get: f(x) = (x-√5)(x+√5)(x-7).

Answer 2

`p(x)=x^3-7x^2-5x+35`

Step-by-step explanation:

The required cubic equation has roots
`x=√(5) ,x=-√(5)` and
`x=7`

This implies that the cubic function has roots
`(x-√(5) )`,
`(x+√(5) )` and
`(x-7)`.

Let p(x) be the cubic function, then we can write the factored form as:

`p(x)=(x-√(5))(x+√(5))(x-7)`

We apply difference of two squares to the first two factors to get:

`p(x)=(x^2-(√(5))^2)(x-7)`

`p(x)=(x^2-5)(x-7)`

We expand using the distributive property to get:

`p(x)=x^2(x-7)-5(x-7)`

`p(x)=x^3-7x^2-5x+35`