Respuesta :
Answer:
The possible length and width are (2x-1) and (11x-2).
Step-by-step explanation:
We are given that,
Area of the rectangular blanket = [tex]22x^{2}-7x-2[/tex].
As, the area of a rectangle = Length × Width.
We need to find the factors of the polynomial [tex]22x^{2}-7x-2[/tex].
The solution of the equation [tex]ax^{2}+bx+c=0[/tex] is [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].
So, the solution of [tex]22x^{2}-7x-2=0[/tex] is given by,
[tex]x=\frac{7\pm \sqrt{(-7)^2-4\times 22\times (-2)}}{2\times 22}[/tex]
i.e. [tex]x=\frac{7\pm \sqrt{49+176}}{44}[/tex]
i.e. [tex]x=\frac{7\pm \sqrt{225}}{44}[/tex]
i.e. [tex]x=\frac{7\pm 15}{44}[/tex]
i.e. [tex]x=\frac{7+15}{44}[/tex] and [tex]x=\frac{7-15}{44}[/tex]
i.e. [tex]x=\frac{22}{44}[/tex] and [tex]x=\frac{8}{44}[/tex]
i.e. [tex]x=\frac{1}{2}[/tex] and [tex]x=\frac{2}{11}[/tex]
Thus, the factors of the corresponding polynomial are (2x-1) and (11x-2).
That is,
Area of a rectangle = [tex]22x^{2}-7x-2[/tex] = (2x-1) × (11x-2).
Hence, the possible length and width are (2x-1) and (11x-2).
