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:

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8 0

2 years ago

Regina went out for breakfast. The bill came to $7.12. If Regina has a discount coupon for 20%, how much will be taken off the b

PolarNik [594]

I believe $1.42 would be taken off of the bill:))

3 0

3 years ago

Read 2 more answers

There are 6 people on the planning committee.two of them missed the last meeting what fraction of the planning committee was abs

natka813 [3]

Easy, so there are six people, 2 went absent, so there are 4 people left
so the answer would be 4/6

your welcome

5 0

3 years ago