Question

If a polynomial function f(x) has roots 6 and square root of 5, what must also be a root of f(x)?

Answer 1

Answer:

-$\sqrt{5}$

Step-by-step explanation:

A root with square root or under root is only obtained when we take the square root of both sides. Remember that when we take a square root, there are two possible answers:

• One answer with positive square root
• One answer with negative square root

For example, for the equation:

$x^{2}=3$

If we take the square root of both sides, the answers will be:

$x=\sqrt{3} \text{ or } x= -\sqrt{3}$

Only getting one solution with square root is not possible. Solutions with square root always occur in pairs.

For given case, the roots are 6 and $\sqrt{5}$. Therefore, the 3rd root of the polynomial function f(x) had to be -$\sqrt{5}$

It seems you made error while writing option B, it should be - square root of 5.