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elena55 [62]
2 years ago
7

Find the sum and product of the roots of each equation of

="2x^{2}" alt="2x^{2}" align="absmiddle" class="latex-formula"> - 8x + 8 = 0
Mathematics
1 answer:
vlada-n [284]2 years ago
5 0

Answer:  Sum (b) = -4

               Product (c) = 4

<u>Step-by-step explanation:</u>

In the quadratic equation ax² + bx + c

  • b represents the sum of the roots
  • c represents the product of the roots

 2x² - 8x + 8 = 0

2(x² - 4x + 4 = 0)

       ↓        ↓

     b= -4   c= 4

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A gardener wants to create a rectangular vegetable garden in a backyard. She wants it to have a total area of 120 square feet, a
erastova [34]
Comment
This is an area problem. The key words are 120 square feet and 12 feet longer.
And of course width is a key word when you are reading this.

Formula
Area = L * W

Givens
W = W
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Substitute and Solve
Area = L* W
120 = W*(W + 12)
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This does not factor easily. I would have thought that a graph might help but not if the dimension has to be to the nearest 1/100 of a foot. The only thing we can do is use the quadratic formula.

a = 1
b = 12
c = - 120

w = [ -b +/- sqrt(b^2 - 4ac) ]/(2a)
w = [-12 +/- sqrt(12^2 - 4*(1)(-120)] / 2*1
w = [-12 +/- sqrt(144 - (-480)]/2
w = [-12 +/- sqrt(624)] / 2
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w = (12.979992) / 2
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L = w + 12
L = 6.489995 + 12
L = 18.489995

check
Area = L * W
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Answer
L = 18.489995 = 18.49 feet
W = 6.489995 = 6.49 feet

Note: in the check if you round first to the answer, LW = 120.0001 when you find the area for the check. Kind of strange how that nearest 1/100th makes a difference.
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