Download PTU B.Sc (Non-Medical) 2020 March 2nd Sem 76304 Theory Of Equations Question Paper

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Roll No. Total No. of Pages : 02
Total No. of Questions : 09

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

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1) Write briefly :

1. What do you mean by rate of convergence?
2. What is the nature of convergence of Newton’s method?
3. Define floating point number.
4. If there is only one change in sign in f (x), then how many positive root (s) will f(x)have?

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5. Find the absolute error if the number X= 0.00545828 is truncated to three decimal digits.
6. Without actual division, find the remainder when x⁴ + 6x³ — 5x + 3 is divided by x + 2.
7. Form an equation whose roots are the roots of the equation x⁴ —3x³ + 7x — 1 = 0 with their signs changed.
8. Find the roots of the equation x³ —12x² + 44x — 48 = 0, given that the roots are in A.P.
9. Use synthetic division to compute f(5) where f (x) =x⁴ — 4x³ - 7x² + 11x — 13.

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10. Show that x⁴ +3x + 2 = 0 has two non-real roots.

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SECTION-B

2. Discuss various types of errors and their sources.
3. Solve x³ —27x + 54 = 0 using Cardan’s method.

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4. Solve x⁴ + 15x³ + 70x² + 120x + 64 = 0 when the roots are in G.P.
5. Find the iterative formula or finding vN , where N is a real number, using Newton-Raphson formula. Hence evaluate v28 .
6. Find the equation whose roots exceed by 2 the roots of the equation 4x⁴ +32x³ + 83x² + 76x + 21 = 0. Hence find the roots of the equation.

SECTION-C

7. Solve the equation x⁴ - 120x² + 54x² + 96x +40=0 by Ferrari’s method.

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8. 1. Show that the equation 2x⁴ + 3x³ + 3x + k = 0.has at least four imaginary roots for all values of k.
   2. If the product of two roots of x⁴ + px³+ qx² + rx + s = 0 is equal to the product of the other two. then show that r² = p²s.
9. 1. Find a root of the equation x² —5=0 using secant method correct to three places of decimal.
   2. Use the iteration method to find a root of the equation x² + x — 100 = 0, correct to four decimal places.

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NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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