the-equation-f-x-0-has-real-roots-in-the-interval-a-b-if-A-f-a-gt-0-and-f-b-gt-0-B-f-a-lt-0-and-f-b-lt-0-C-f-a-gt-0-and-f-b-0-D-f-a-gt-0-and-f-b-lt-0-

Question Number 66226 by Rio Michael last updated on 11/Aug/19

$${the}\:{equation}\:\:{f}\left({x}\right)=\mathrm{0}\:{has}\:{real}\:{roots}\:{in}\: \\ $$$${the}\:{interval}\:\left({a},\:{b}\right)\:{if} \\ $$$${A}\:\:\:\:−{f}\left({a}\right)>\mathrm{0}\:\:{and}\:{f}\left({b}\right)\:>\mathrm{0} \\ $$$${B}\:\:\:{f}\left({a}\right)\:<\mathrm{0}\:{and}\:{f}\left({b}\right)\:<\mathrm{0} \\ $$$${C}\:\:−{f}\left({a}\right)\:>\mathrm{0}\:\:{and}\:{f}\left({b}\right)\:=\mathrm{0} \\ $$$${D}\:\:{f}\left({a}\right)\:>\mathrm{0}\:\:{and}\:{f}\left({b}\right)\:<\:\mathrm{0} \\ $$

Commented by Prithwish sen last updated on 11/Aug/19

$$\mathrm{A}\:\mathrm{and}\:\mathrm{D} \\ $$

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