Algebra Exercises

May 29th, 2015
Studypool Tutor
Price: \$10 USD

Tutor description

1. The number of real roots of the equation ecosx - e-cosx 4 = 0 is(A)0(B) 1(C) 2(D) None of these 1. (A) ecosx = t Þ t2 –4t – 1 = 0 Þ t = ecosx = 2 ± Ö5 Since ecosx Î [1/e, e], so number of real roots is 0. 2. The number of real

Word Count: 7405
Showing Page: 1/37
QEEGroup I1.The number of real roots of the equation ecosx - e-cosx4 = 0 is(A)0(B)1(C)2(D)None of these1.(A)ecosx = tt2 4t 1 = 0t = ecosx = 2 5Since ecosx [1/e, e], so number of real roots is 0.2.The number of real roots of the quadratic equation (n > 1) is (A) 1 (B) 2(C) n(D) 02.(D) Each term of is non-negative, so no real root.3.The set of values of a for which the equation x3 3x + a has three distinct real roots, is(A) ( -, ) (B) (-2, 2)(C) ( -1, 1) (D) none of these 3.(B) Let f(x) = x3 3x +a f(x) = 3x2 3.For three distinct real roots (i) f(x) = 0 should have two distinct real roots and and (ii) f() f() < 0 Here = 1, = 1. Now f() f() < 0 (1 3 + a) (1+ 3 + a) < 0 (a 2) (a + 2) < 0 2 < a < 2.4.If a1, a2, a3 (a1 > 0) are in G. P. with common ratio r, then the value of r, for which the inequality 9a1 + 5 a3 > 14 a2 holds, can not lie in the interval(A) [1, ) (B) [1, 9/5](C) [4/5, 1](D) [5/ 9, 1]4.(B) Since a1, a2, a3 (a1 > 0) are in G.P. So, a2 = a1 r ; a3 = a1 r2 Given inequality 9a1 + 5 a3 > 14 a29 a1+ 5 a1 r2 > 14 a1r 5r2 14 r +9 > 0 (r 1) ( r 9/5) > 0 r > 9/ 5 and r < 1 r [1, 9/ 5]. 5.Consider the graph of f(x) = ax2 +bx +c in the adjacent figure. We can conclude that (A) c >

Review from student

Studypool Student
" Good stuff. Will use again. "

1820 tutors are online

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors