Respuesta :
The width of the walkaway be 4 feet.
What is Discriminant Formula?
The discriminant formula is used to determine the nature of the roots of a quadratic equation. The discriminant of a quadratic equation[tex]ax^{2} +bx+c=0[/tex] is D =[tex]b^{2} -4ac[/tex]
If D > 0, then the equation has two real distinct roots.
If D = 0, then the equation has only one real root.
Given that: [tex]Area\; of \;walkway,\; a(w)\;= 4w^{2} + 100 w[/tex]
also, area of walkaway = 464 square feet.
So, [tex]4w^{2} + 100 w =464[/tex]
[tex]4w^{2} + 100 w -464=0[/tex]
Using Discriminant method,
a=4, b=100, c=-464
[tex]w= \frac{-b\pm\sqrt{b^{2}-4ac} }{2a}[/tex]
w= [tex]\frac{-100\pm\sqrt{(100)^{2}-4*4*(-464)} }{2*4}[/tex]
w= [tex]\frac{-100\pm\sqrt{17424} }{8}[/tex]
So, [tex]w_1= \frac{-100+\sqrt{17424} }{8} \;\;\;\; w_2= \frac{-100-\sqrt{17424} }{8}[/tex]
[tex]w_1= \frac{-100+132 }{8} \;\;\;\; w_2= \frac{-100-132}{8}[/tex]
[tex]w_1 = 4 \;\;\;\; and \;\;\; w_2= -29[/tex]
Hence the width of the walkaway be 4 feet.
Learn more about discriminant formula here:
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