Answer:
The length of the sign is \((4x-5)\) inches
Step-by-step explanation:
We are given that,
Area of the square design = \(16x^2-40x+25\)
We will first find the roots of the equation \(16x^2-40x+2=0\)
The roots of the quadratic equation \(ax^2+bx+c=0\) are given by \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
On comparing, a= 16, b= -40 and c= 25
So, the roots of the equation are,
\(x=\frac{40\pm\sqrt{(-40)^2-4\times 16\times 25}}{2\times 16}\)
i.e. \(x=\frac{40\pm\sqrt{1600-1600}}{32}\)
i.e. \(x=\frac{40\pm\sqrt{0}}{32}\)
i.e. \(x=\frac{40}{32}\)
i.e. \(x=\frac{5}{4}\)
That is, the factors of the polynomial \(16x^2-40x+25\) are \((4x-5)\) and \(4x-5\).
So, Area of the square design = \(16x^2-40x+25\) = \((4x-5)^2\)
Since, Area of a square = \(Length^2\)
Thus, the length of the sign is \((4x-5)\) inches
