A polynomial equation with rational coefficients has the roots:

(5 - √1) and (4 + √7)

Step-by-step explanation:

Here we have 4 roots, then this is a polynomial of 4th degree.

We can write it as

a*x⁴ + b*x³ + c*x² + d*x + e = 0

We could rewrite this as the product of two quadratic equations:

(a₁*x² + b₁*x + c₁)*(a₂*x² + b₂*x + c₂) = 0

This will be equal to zero when (a₁*x² + b₁*x + c₁) is equal to zero, and when

(a₂*x² + b₂*x + c₂) is equal to zero.

Then we need to find the roots of these two quadratic equations.

And we know that the roots of a quadratic equation like:

a₁*x² + b₁*x + c₁ are given by:

Then the general form of the roots is something like:

This means that if one of the roots is:

5 + √1, we must have another root equal to 5 - √1

And if we have one root equal to 4 - √7, then we must have another root equal to 4 + √7

Then the correct options are:

(5 - √1) and (4 + √7)

8.75

how-to:

first, we need to find what we have to work with.

since i know that we have 7 (years) and 0.8 (inches), we can use these to solve and find the equation!

secondly, what you want to do, is see that we need to know how much growth out of the 0.8 inches he got in only 1 year, instead of 7 years.

let's try to divide.

7 ÷ 0.8 = 8.75