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Title: Prove that x^4 + 2x^3 −x = 1 has at least two real roots. Post by: gurjot kaur on Apr 17, 2020 Prove that x4 + 2x3 −x = 1 has at least two real roots.
Title: Prove that x^4 + 2x^3 −x = 1 has at least two real roots. Post by: bio_man on Apr 17, 2020 Prove that x4 + 2x3 −x = 1 has at least two real roots. Have you tried using Descartes’ Rule of Signs? x4 + 2x3 −x = 1 x^4 + 2x^3 + 0x^2 - x - 1 = 0 The number of positive real zeros of f is equal to the number of variations in sign of f(x) or is less than the number of variations in sign of f(x) by a positive even integer. If f(x) has one variation in sign, then f has exactly one positive real zero. The number of negative real zeros of f is equal to the number of variations in sign of f(-x) or is less than the number of variations in sign of f(-x) by a positive even integer. If f(-x) has one variation in sign, then f has exactly one negative real zero https://www.youtube.com/watch?v=Hl0j_a9WVks You may also need to apply: Fundamental Theorem of Algebra: Every polynomial function of degree n>=1 has at least one complex zero. Number of Zeros Theorem: Every polynomial of degree n has n complex zeros provided each zero of multiplicity greater than 1 is counted accordingly. |