What is 4x² / 4x² ? Is the answer still a polynomial?
2 answers:
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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.
Answer: Maximum height = 105 feet
And, It takes 9/4 seconds to reach that point.
Step-by-step explanation:
Here the given function that shows the height of the pumpkin,
--------(1)
Where t is the time in second.
Differentiating equation (1) with respect to t,
We get,
Again differentiating above equation with respect to t,
We get,
For maximum or minimum,
At t = 9/4 , h''(t) = Negative value,
Therefore, At t = 9/4 seconds, h(t) is maximum,
And, the maximum value is,
Therefore, the maximum height of the pumpkin is 105 feet at 9/4 seconds