Answer: y= 3 or -2/3
Step-by-step explanation:
I think you mean "if the points <span>(2,5), (3,2) and (4,5) satisfy an unknown 3rd degree polynomial, what is the polynomial?"
Since 3 roots {2, 3, 4} are known, we might begin by assuming that this poly would have the form y = ax^3 + bx^2 + cx + d (which has three factors). Unfortunately, three roots are not enough to determine all four constants {a, b, c, d}.
So, let's assume, instead, that the poly would have the form y = ax^2 + bx + c. Three given points should make it possible to determine {a, b, c}.
(2,5): 5 = a(2)^2 + b(2) + c => 5 = 4a + 2b + c
(3,2): 2 = a(3)^2 + b(3) + c => 2 = 9a + 3b + 5 - 4a - 2b
(4,5): 5 = a(4)^2 + b(4) + c => 5 = 16a + 4b + 5 - 4a - 2b
Now we have two equations in a and b alone, which enables us to solve for a and b:
</span>2 = 9a + 3b + 5 - 4a - 2b becomes -3 = 5a + b
<span>and
</span>5 = 16a + 4b + 5 - 4a - 2b becomes 0 = 12a + 2b, or 0 = 6a + b, or 0=-6a-b
<span>
Adding this result to -3 = 5a + b, we get -3 = -a, so a =3.
Thus, since -3 = 5a + b, -3 = 5(3) + b, so b = -18
All we have to do now is to find c. Let's do this using </span>5 = 4a + 2b + c.
We know that a = 3 and b = -18, so this becomes 5 = 4(3) + 2(-18) + c.
Thus, 5 = 12 - 36 + c, or c = 29.
With a, b and c now known, we can write the poly as y = 3x^2 - 18x + 29.
Now the only thing to do remaining is to verify that each of the three given points satsifies y = 3x^2 - 18x + 29. Try this, please.
The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
According to the statement
We have a given that the maximum sum of the positive integers is 400.
And we have to find the value of n which is a maximum number of integers by which the value of sum become 400.
So, to find the value of the n we use the
A.P. Series'Summation formula
According to this,
S = n (n+1)/2
Here the value of s is 401
Then
S = n (n+1)/2
401 = n (n+1)/2
401*2 = n (n+1)
802 =n (n+1)
n (n+1) = 802
n^2 + n -802 =0
By the use of the Discriminant formula the
value of n becomes n = -28 and n = 27.
The negative value of n is neglected.
Therefore the value of n is 27.
So, The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
Learn more about maximum number of integers here brainly.com/question/24295771
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