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Question
the equation x⁴ -594= ax³ + bx² + cx has exactly 3 distinct integral roots. if a, b and c are real numbers, then answer the following questions
the equation x⁴ -594= ax³ + bx² + cx has exactly 3 distinct integral roots. if a, b and c are real numbers, then answer the following questions
1. find largest value of b
2. find minimum possible value of a
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Answer
let roots be r1 r2 r3
sum of roots b
r1r2r3+ r1r3^2+ r2r3^2= c
product r1.r2.r3^2 =d
trial and error r1=1 r2=6 r3=3
a=13
b=36
(Chatgpt)
