jdd0518

14.06.2020 •

Mathematics

Mr. Blake builds a brick border on all
sides of a patio,
shaped like
square. If the
length of each of
the border is 10
ft., What is its
perimeter.

Solved

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Ответ:

yuvin

10.10.2022

Mathematics

$x=0, multiplicity\ 1\\x=-2, multiplicity\ 1\\x=-3, multiplicity\ 1$

Step-by-step explanation:

we have

$f(x)=3x^{3}+15x^{2} +18x$

To find the zeros of the function equate to zero

$3x^{3}+15x^{2} +18x=0$

Factor the term 3x

$3x(x^{2}+5x+6)=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2}+5x+6=0$

$a=1\\b=5\\c=6$

substitute in the formula

$x=\frac{-5(+/-)\sqrt{5^{2}-4(1)(6)}} {2(1)}$

$x=\frac{-5(+/-)\sqrt{25-24}} {2}$

$x=\frac{-5(+/-)1} {2}$

$x=\frac{-5+1} {2}=-2$

$x=\frac{-5-1} {2}=-3$

$x^{2}+5x+6=(x+2)(x+3)$

substitute

$3x(x^{2}+5x+6)=3x(x+2)(x+3)$

The zeros are

$x=0, multiplicity\ 1\\x=-2, multiplicity\ 1\\x=-3, multiplicity\ 1$

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Mr. Blake builds a brick border on allsides of a patio,shaped likesquare. If thelength of each ofthe border is 10ft., What is itsperimeter.