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storchak [24]
3 years ago
8

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

Mathematics
1 answer:
ivolga24 [154]3 years ago
4 0

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.

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A and b are monomials where a = 125 and b = 27p12. what is the factored form of a – b?
torisob [31]

The factored form of a - b is \left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right).

<h3>What is monomial factorization ?</h3>

A monomial is an expression that is the product of constant and non-negative integer powers of x, like 3x^{2}..

A monomial is expressed as a product of two or more other monomials when it is factored.

Here,

a = 125

$b=27 p^{12}$

To find: a - b

a - b = 125 - 27 p^{12}$

a - b =  5^{3}-\left(3 p^{4}\right)^{3}$

We know that,

$x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$

Finding the factored form of a - b using this method:

$a - b=\left(5-3 p^{4}\right)\left(5^{2}+5\left(3 p^{4}\right)+\left(3 p^{4}\right)^{2}\right)$

$a-b=\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$

So, factored form of a - b is $\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$.

Learn more about monomial factorization here:

brainly.com/question/26278710

#SPJ4

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