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1) The solution for m² - 5m - 14 = 0 are x=7 and x=-2.
2)The solution for b² - 4b + 4 = 0 is x=2.
<u>Step-by-step explanation</u>:
The general form of quadratic equation is ax²+bx+c = 0
where
- a is the coefficient of x².
- b is the coefficient of x.
- c is the constant term.
<u>To find the roots :</u>
- Sum of the roots = b
- Product of the roots = c
1) The given quadratic equation is m² - 5m - 14 = 0.
From the above equation, it can be determined that b = -5 and c = -14
The roots are -7 and 2.
- Sum of the roots = -7+2 = -5
- Product of the roots = -7
2 = -14
The solution is given by (x-7) (x+2) = 0.
Therefore, the solutions are x=7 and x= -2.
2) The given quadratic equation is b² - 4b + 4 = 0.
From the above equation, it can be determined that b = -4 and c = 4
The roots are -2 and -2.
- Sum of the roots = -2-2 = -4
- Product of the roots = -2
The solution is given by (x-2) (x-2) = 0.
Therefore, the solution is x=2.
The partial blueprint of a house that includes 3 bedrooms is shown below. The scale is 2.75 inches : 3 feet. What is the actual length and width of Bedroom 3 in feet?
Bedroom 1 w=9.17; l= 11 in
Bedroom 2 w=7.33 in; l= 12.83
Bedroom 3 w= 11 in; l= 14.67 in
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2.75 inches : 3 or 2.75 in / 3 feet
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Can you see the updates?
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Bedroom 3 w= 11 in; l= 14.67 in
11 in * 3 feet / 2.75 in = 12 feet
14.67 in 3 feet / 2.75 in = 16 feet
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Answer
Bedroom 3 w= 12 ft ; l= 16 ft
