Answer:
The answer is -√7
Step-by-step explanation:
∵ The polynomial has roots 3 and √7
∴ It must have root -√7 the conjugate of √7
∴ The roots of f(x) are 3 , √7 , -√7
(one rational and two irrational conjugate to each other)
Answer: -√7 must also be a root of f(x).
Step-by-step explanation: Given that a polynomial function f(x) has roots 3 and radical 7.
We are to find the other number that must be a root of f(x).
We know that
irrational roots of a polynomial function always occur in conjugate pairs.
That is, if (a + √b) is a root of a polynomial function, then its conjugate pair (a - √b) is also a root of the polynomial function.
For the given polynomial f(x), the given roots are 3 and √7.
Now, [tex]\sqrt7=0+\sqrt 7.[/tex]
Then, the other root will be
[tex]0-\sqrt7=-\sqrt7.[/tex]
Thus, -√7 must also be a root of f(x).
