SOLUTION: hi these question are from a worksheet....plzz kindly help
1) A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the law
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Question 204190: hi these question are from a worksheet....plzz kindly help
1) A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and flower bed is 165m². What is the width of the flower bed?
Let x be the width of the flowerbed
(8+2x)(4+2x)=165
2) Can x (x – 5) = 0 be solved by dividing both sides of the equation by x?
Explain your answer.
3)Write a quadratic equation whose roots are 5 and –3.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
1)
Starting with:
Expand and rearrange the left side.
Subtract 165 from both sides.
Solve this quadratic equation using the quadratic formula: where: a = 4, b = 24, and c = -133.
or
or Discard the negative solution as the width of the flower bed can only be a positive quantity.
The width of the flower bed is 3.5 feet.
------------------------------
2) Can be solved by dividing both sides by x?
No, because you would get olny one of the solutions to this quadratic equation when, in fact, there are really two solutions!
Here's how you would solve it:
Apply the zero product rule: If then either or or both.
or
If then
-----------------------------------
3) Write a quadratic equation whose roots are:
and If these are the roots, then the factors are:
and Multiply these two factors together to get the original quadratic equation.
Multiply using FOIL.
Simplify.
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