Answer:
(b) [tex](x-5)^2(x+2) = 0[/tex] has root 5 of multiplicity 2 and root -2 with multiplicity 1.
Step-by-step explanation:
Here, the given expression is: [tex](x-5)^2(x+2) = 0[/tex]
Now, here as we can see from the given expression,
It has 2 roots.
[tex](x-5)^2(x+2) = 0 \implies (x-5)(x-5)(x+2) = 0[/tex]
⇒ 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 [tex](x-5)^2 = 0[/tex]
and, -2 is a root of multiplicity 1 as ( x + 2) = 0
Hence, [tex](x-5)^2(x+2) = 0[/tex] has root 5 of multiplicity 2 and root -2 with multiplicity 1.
