If a, b are the roots of x + px + 1O and c, d are the rootsof x? + qx + 1 = 0, then the value of (a – (C) (b – (C) (a +|(D) (b + (D) is(A) p² – q²(C) q² + p²(B) q² – p?(D) none of these

Answered: If a, b are the roots of x2 + px + 1 =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Select all expressions that are equivalent to x-4-32 A (x-16*x+2x 8.(x+2*x-16) -CH-S*X+4) D.(x+8xx-4) E (x+4*x-8) Etx-4*x+8) 3. Select all solutions to the equation (2x - 4x + 5) = 0 A1=-= 8x== Cx=22 0.x = 2 b) Sections with are optional Ex = -5 F.x=3 4. Show that (3x - 1Xxx + 5) is equivalent to 3x² + 14x-5 height (feet) E60302 SU 10 5. The height of a sortbail in feet, is modeled by the function is given by h(ty = 3+55:- 16r, where is the time, in seconds, after the softball is hit. A graph of the function is shown. time (seconds) a. About when does the softball reach its maximum height? b. About how high is the maximum height of the softball? 6 Here is a graph that represents a quadratic function which equation could de this function? About when does the ball hit the ground? Ax=(x-2*x + 3) 8.y=(x-2x-3) V x=(x+26x31 D. x = (x + 2x-3) 7. Salve the equation 2x - 7x-15 = 0 Explain or show your work 8. Complete the long division problem to find the quotient of 1,651 and 13 1 13
Find two First terms whose product is ax?: (Ox + )Cx + ) = ax? + bx + c.
6. List all polynomials of the form x++bx+cx²+dx+e with rational coefficients that are factors of the polynomial, x¹²-1.
4. Find the roots of the following over C (a) x2 + 18x+97 (b) x3 + 3x2 – 6x-8 yes that is a cubic (c) 2x2 - 17x - 31 (d) 12x3 - 32x2 + 11x + 15 yes that is also a cubic
I need a quick solution within 15 minutes With my best wishesTon.
If a and ß are the roots of the equation x² – 3x + 4 = 0, the equation whose roots are a? + a + 1 and B² + B + 1 is (a) x' - 6x + 19 = 0 (b) х? + 6х - 37 %3D 0 (c) x' + 6x - 19 = 0 (d) x² - 6x + 37 = 0 If a, and B, are the roots of the equation 3x? - 2x – 5 = 0 and a, and B, are the roots of the equation 2x² + x - 7 = 0, the equation whose roots are (a,a, + B,B,) and (a,ß, + a,B,) is (a) 36x? – 12x + 911 = 0 (b) 9х* - 91х + 11 %3D0 (c) 36x? + 12x - 911 = 0 (d) 9x² + 91x – 19 = 0 3x-2 If a and B are the roots of the equation 7X- 3 5x 1 = 4, 1 is
State true or false with brief justification If ß, and ß, are two 10™ roots of unity, then Q(B) = Q(B,).
XX
If a, ß be the roots of ax² + 2bx + c = 0 and a +8, B+ 8 be those of Ax² + 2Bx+C =0, then 6² 2 ac the value of is - AC A² (a) q² (c) 0 A 2 B² - - (b) (d) 1
3 The roots of the equation x-4x +9 -0 are 2) 2+ /5 3) 2+1/13 4) 2 13
b) The polynomial, fW) =2x" +mz -3, where m and n are real constants, is divisible by (x+1) but leaves a femiAder remainder of 156 when divided by (X-3). Find the valves of n and m.
Given that the equation z2 + (p + iq)z +r + is = 0, where p, q, r, s are real and non-zero has a real root, then how are p, q, r and s related?

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If a, b are the roots of x2 + px + 1 = 0 and c, d are the roots а, of x? + qx + 1 = 0, then the value of (a – (C) (b – (C) (a + (D) (b + (D) is (B) q² – p² (A) p² – q? (C) q² + p² (D) none of these