Fabulous question.
If we have an equation of the form ax^{4} + bx^{3} + cx^{2} + dx + 3 = 0 with
Roots p, q, r and s.
We can say sum of the roots p + q + r + s = .
Sum of the products taken two at a time pq + pr + ps + qr + qs + rs = 𝑐.
Sum of the products taken three at a time pqr + pqs + prs + qrs = .
Product of the roots pqrs = 𝑒.
Note 1: We alternate between - and +
Note 2: Start with the immediate lower power for sum of roots, stick a
negative symbol and then alternate.
So, if p, q, r, s were roots of this equation
P + q + r + x = 4,
Pqrs = 1
Or, Arithmetic mean of p,q, r, s = 1 and geometric mean of pqrs = 1.
P, q, r s are positive real numbers. AM = GM. What does this mean?
This means that all 4 numbers are equal.
Or, this expression is (x-1)^{4}
a = pq + pr + ps + qr + qs + rs = 6
-(-b) = pqr + pqs + prs + qrs = 4
A = 6, b = 4. A + b = 10
Correct Answer: D. 10
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