MathDB

7

Part of 2021 ISI Entrance Examination

Problems(1)

Finding Bounds on Roots

Source: ISI 2021 P7

7/18/2021
Let a,b,ca, b, c be three real numbers which are roots of a cubic polynomial, and satisfy a+b+c=6a+b+c=6 and ab+bc+ca=9ab+bc+ca=9. Suppose a<b<ca<b<c. Show that 0<a<1<b<3<c<4.0<a<1<b<3<c<4.
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