Question

find a quadratic polynomial each with the given numbers as the sum and products of its zeroes respectively.....1/4,-1

Answer 1

A quadratic in the form of ax2+bx +c = 0 has sum of roots: −b/a and
product of roots: c/a.

Sum of roots:
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-b/a = 1/4
-a = 4b
a = -4b
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Product of roots:
c/a = -1/1
c = -a
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Let b = -1. Then a = 4 and because c = -a, then c = -4.
The coefficients of a, b, and c are: 4, -1, and -4 or a multiple of those 3.

4x^2 -1 x - 4 = 0

Answer 2

2 months ago? and it's still open....

Answer 3

For fuzzy bunnies and giggles, here's a better answer:

For a polynomial \(P(x)\), we have \(P(x)=(x-r_1)(x-r_2)=x^2-(r_1+r_2)x+r_1r_2\).
Therefore, our polynomial is \(x^2-\frac{1}{4}x-1=4x^2-x-4\).