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Let b, c E R and b>1+c. Show that the following equation has two distinct real solutions: r2 + bx +c =0. Hint: consider two cases: c<0 and c>0.

Let b, c E R and b>1+c. Show that the following equation has two distinct real solutions: r2 + bx +c =0. Hint: consider two cases: c<0 and c>0.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let b, cE R and b>1+c. Show that the following equation has two distinct real solutions: x2 + bx + c=0. Hint: consider two cases: c<0 and c >0. Let A, B, C and D be sets. Prove that if A x B and C × D are disjoint, then either AnC=Ø or BND=Ø. Hint: use proof by contradiction. Consider two functions f : Z→Z × Z given by f(n) = (n – 1, n) , and g: Z x Z→ Q Q3 given by g(a, b) : a · b Let h = go f. (a) Is h injective? (b) Is h surjective? Justify your answer. Q4 Let ¤1 V2, xn+1= v2ªn, n>1. Use induction to show that xn <2 for all n E N. Suppose that n, m are two integers, both not divisible by 7. Prove that n2 + m² is not divisible Q5 by 7.
Transcribed Image Text:Let b, cE R and b>1+c. Show that the following equation has two distinct real solutions: x2 + bx + c=0. Hint: consider two cases: c<0 and c >0. Let A, B, C and D be sets. Prove that if A x B and C × D are disjoint, then either AnC=Ø or BND=Ø. Hint: use proof by contradiction. Consider two functions f : Z→Z × Z given by f(n) = (n – 1, n) , and g: Z x Z→ Q Q3 given by g(a, b) : a · b Let h = go f. (a) Is h injective? (b) Is h surjective? Justify your answer. Q4 Let ¤1 V2, xn+1= v2ªn, n>1. Use induction to show that xn <2 for all n E N. Suppose that n, m are two integers, both not divisible by 7. Prove that n2 + m² is not divisible Q5 by 7.
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