\textrm{if the equation \: \: }x^4 + px^3 +qx^2 + rx+ 5= 0 \textrm{\: \: has four positive real roots find minimum value of pr }
2)
without use of CALCULUS prove that
\textrm{if the equation \: \: } x^3 +ax+ b= 0 \textrm{\: \: has only real roots}
\textrm{prove that } \, \, 4a^3 + 27b^2\leq 0
( practice probs for maths enthusiasts)
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2 Answers
1p=-(a+b+c+d)
r=-(abc+bcd+abd+acd)
a,b,c,d r roots
pr=abcd(a+b+c+d)(1/a+1/b+1/c+1/d)≥16abcd(a.m-h.m)
abcd=5
so pr≥80