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Identify the roots of the equation and the multiplicities of the roots. HELP ASAP!!

Identify the roots of the equation and the multiplicities of the roots. HELP ASAP-example-1

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Answer:

(b)
(x-5)^2(x+2) = 0 has root 5 of multiplicity 2 and root -2 with multiplicity 1.

Explanation:

Here, the given expression is:
(x-5)^2(x+2) = 0

Now, here as we can see from the given expression,

It has 2 roots.


(x-5)^2(x+2) = 0  \implies (x-5)(x-5)(x+2) = 0

⇒ Either ( x- 5) = 0, or ( x + 2) = 0

⇒ either x = 5 or x = -2

So, x =5 and x = -2 are the ONLY TWO ROOTS of the given expression.

Now, 5 is a root of multiplicity 2 as
(x-5)^2  = 0

and, -2 is a root of multiplicity 1 as ( x + 2) = 0

Hence,
(x-5)^2(x+2) = 0 has root 5 of multiplicity 2 and root -2 with multiplicity 1.

User Amit Gupta
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