Answer:
f(x) = x^2 - 3x + 1.
Step-by-step explanation:
If the roots of this polynomial are 1 and 2, the corresponding factors are (x - 1) and (x - 2). Multiplying, we get
f(x) = (x - 1)(x - 2) = x^2 - 3x + 1
The polynomial of least degree with roots 1 and 2 is f(x) = x^2 - 3x + 1.
So let's take a peek at both's ages, keep in mind, every year, is 1year added to Irene and 1year added to Fred
so... if we look at their ages

notice, Fred is always 40years older than Irene
thus, whatever age Irene is, let's say "i", then Fred is " i + 40 "
now, when is Fred 5 times Irene's age or 5*i or 5i? well,
f = fred's age i = irene's age
f = i + 40
now if f = 5i
5i = i + 40 <--- solve for "i" to see how old Irene was then
Check the picture below.
since in a rhombus the diagonals bisect each other, thus EC = EA.
now, the rhombus is simply 4 congruent triangles, we know the base and height of one of them, thus
![\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=8\\ h=15 \end{cases}\implies A=\cfrac{1}{2}(8)(15)\implies A=60 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of all 4 triangles}}{4(60)\implies 240}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20triangle%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B2%7Dbh~~%20%5Cbegin%7Bcases%7D%20b%3D8%5C%5C%20h%3D15%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B2%7D%288%29%2815%29%5Cimplies%20A%3D60%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20all%204%20triangles%7D%7D%7B4%2860%29%5Cimplies%20240%7D)
<span>When a = 3 and b ≠ 5, the system will be inconsistent because the lines will be parallel. When a = 3 and b = 5, the system will be consistent and dependent because they represent the same line.</span>