Question

The martinez family has a walkway around their swimming pool. the area of the walkway can

Answer 1

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$ax^{2} +bx+c=0$ is D =$b^{2} -4ac$

If D > 0, then the equation has two real distinct roots.

If D = 0, then the equation has only one real root.

Given that: $Area\; of \;walkway,\; a(w)\;= 4w^{2} + 100 w$

also, area of walkaway = 464 square feet.

So, $4w^{2} + 100 w =464$

     $4w^{2} + 100 w -464=0$

Using Discriminant method,

a=4, b=100, c=-464

$w= \frac{-b\pm\sqrt{b^{2}-4ac} }{2a}$

w= $\frac{-100\pm\sqrt{(100)^{2}-4*4*(-464)} }{2*4}$

w= $\frac{-100\pm\sqrt{17424} }{8}$

So, $w_1= \frac{-100+\sqrt{17424} }{8} \;\;\;\; w_2= \frac{-100-\sqrt{17424} }{8}$

$w_1= \frac{-100+132 }{8} \;\;\;\; w_2= \frac{-100-132}{8}$

$w_1 = 4 \;\;\;\; and \;\;\; w_2= -29$

Hence the width of the walkaway be 4 feet.

Learn more about discriminant formula here:

brainly.com/question/2615966

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