Answer:
x^4 -53x^2 +108x +160
Step-by-step explanation:
If <em>a</em> is a zero, then (<em>x-a</em>) is a factor. For the given zeros, the factors are ...
p(x) = (x +8)(x +1)(x -4)(x -5)
Multiplying these out gives the polynomial in standard form.
= (x^2 +9x +8)(x^2 -9x +20)
We note that these factors have a sum and difference with the same pair of values, x^2 and 9x. We can use the special form for the product of these to simplify our working out.
= (x^2 +9x)(x^2 -9x) +20(x^2 +9x) +8(x^2 -9x) +8(20)
= x^4 -81x^2 +20x^2 +180x +8x^2 -72x +160
p(x) = x^4 -53x^2 +108x +160
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The graph shows this polynomial has the required zeros.
Simplify the problem down, so:
m = 12 & n = 5
m = 6 & n = 2.5 <span>(divided each number by 20)
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Now m is a factor of 18. Multiply each number by 3.
Answer: m = 18 & <span>n = 7.5</span>
Here are the answer: a) R = 3.6 and b) A = 2
Step-by-step explanation:
Given,
R is inversely proportional to A.
R ∝ 
so, R =
-------eq 1 where k is any constant
To find the values of a) R when A = 5 and
b) Value of A when R = 9
Now,
Putting R = 12 and A = 1.5 in eq 1 we get,
12 = 
or, k = 12×1.5 = 18
From eq 1 we get,
R =
--------- eq 2
Now,
a) Putting A= 5 in eq 2 we get,
R =
= 3.6
b) Putting R = 9 in eq 2 we get
R =
or, A =
= 2