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    Theory of Equations Sheet-00

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    mo635107
    This document contains a theory of equations quiz with 22 multiple choice questions about finding the quotient and remainder when dividing polynomials. It also contains questions about finding values of variables to satisfy given polynomials and finding the solutions of polynomials within intervals. The document requests the solutions to 3 additional polynomials be provided.

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    © All Rights Reserved
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    Theory of Equations Sheet-00

    Uploaded by

    mo635107
    12 views3 pages
    This document contains a theory of equations quiz with 22 multiple choice questions about finding the quotient and remainder when dividing polynomials. It also contains questions about finding values of variables to satisfy given polynomials and finding the solutions of polynomials within intervals. The document requests the solutions to 3 additional polynomials be provided.

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    Original Title

    Theory of Equations sheet-00 (1)(1)

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    This document contains a theory of equations quiz with 22 multiple choice questions about finding the quotient and remainder when dividing polynomials. It also contains questions about finding values of variables to satisfy given polynomials and finding the solutions of polynomials within intervals. The document requests the solutions to 3 additional polynomials be provided.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    12 views3 pages

    Theory of Equations Sheet-00

    Uploaded by

    mo635107
    This document contains a theory of equations quiz with 22 multiple choice questions about finding the quotient and remainder when dividing polynomials. It also contains questions about finding values of variables to satisfy given polynomials and finding the solutions of polynomials within intervals. The document requests the solutions to 3 additional polynomials be provided.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    Faculty of Engineering

    Basic Engineering Science. Department


    Math 1

    Theory of Equations
    ➢ Choose the correct answer
    2 𝑥 3 +2 𝑥 2 +7
    1) The reminder (R) of is :
    𝑥−2

    a) Zero b) -1 c) 17 d) 31
    2 𝑥 3 +2 𝑥 2 +7
    2) The quotient (Q) of is:
    𝑥−2
    a) 2𝑥 2 + 6𝑥 + 12 b) 12𝑥 2 + 6𝑥 + 2 c) 31 d) −4 + 2𝑥 − 2𝑥 2

    𝑥 5 −3 𝑥 3 +5 𝑥+8
    3) The reminder (R) of is :
    𝑥+1

    a) Zero b) 15 c) 5 d) 11
    𝑥 5 −3 𝑥 3 +5 𝑥+8
    4) The quotient (Q) of is:
    𝑥+1

    a) 𝑥 4 + 6 𝑥 3 + 2𝑥 2 − 5 b) 𝑥 4 − 𝑥 3 − 2𝑥 2 + 2𝑥 + 3
    c)𝑥 4 − 𝑥 3 − 2𝑥 2 + 2𝑥 − 7 d) 𝑥 4 + 𝑥 3 − 2𝑥 2 − 2𝑥 + 3

    2 𝑥 6 −18 𝑥 4 +𝑥 2 −9
    5) The reminder (R) of is :
    𝑥+3

    a) Zero b) 1 c) 7 d) none of above


    2 𝑥 6 −18 𝑥 4 +𝑥 2 −9
    6) The quotient (Q) of is:
    𝑥+3
    a)2𝑥 5 + 6𝑥 4 − 𝑥 2 + 3 b) 2𝑥 5 − 6𝑥 4 + 𝑥 + 3
    c) 2𝑥 5 − 6𝑥 4 + 𝑥 − 3 d) 𝑁𝑜𝑛 𝑜𝑓 𝑎𝑏𝑜𝑣𝑒
    −4 𝑥 4 +5 𝑥 2 +8
    7) The reminder (R) of is :
    𝑥−3
    a) 377 b) -287 c) 271 d) −271
    −4 𝑥 4 +5 𝑥 2 +8
    8) The quotient (Q) of is:
    𝑥−3
    a)−4𝑥 3 − 12𝑥 2 − 31𝑥 − 93 b) −4𝑥 3 + 12𝑥 2 − 31𝑥 + 93
    c) 4𝑥 3 − 12𝑥 2 + 31𝑥 − 93 d) None of above
    2 𝑥 3 +𝑘𝑥 2 −6
    9) Find the value of k to make the reminder of equal 3 :
    𝑥+1
    a) 1 b) 11 c) 25 d) Zero

    1|Page
    Faculty of Engineering
    Basic Engineering Science. Department
    Math 1

    Theory of Equations
    3 𝑥 4 +𝑘 𝑥 2 +7
    10) Find the value of k to make the reminder of equal to the reminder of
    𝑥+1
    𝑥 4 +𝑘 𝑥−6
    :
    𝑥−2

    a) 1 b) 11 c) 25 d) Zero
    2006 2005
    11) What is the remainder when 𝑥 +𝑥 + ⋯ + 𝑥 + 1 is divided by x+1 ?

    a) 1 b) 𝑥 c) Cannot be calculated d) 2006

    12) What is the polynomial yield a reminder of 2 upon division by (x -1), and a
    reminder of 1 upon division by (x -2) ?

    a) 𝑥 2 − 4𝑥 + 5 b) 𝑥 3 + 5𝑥 − 2 c) 𝑥 2 − 25𝑥 + 15 d) None of above

    13) What is the reminder of polynomial in Eq(12) when divided by (x -1)(x-2)?

    a) 1 b) 𝑥 + 3 c) x- 3 d) −𝑥 + 3

    14) What is value of k in the polynomial 𝑥 3 − 2𝑥 2 − 5𝑥 + 𝑘 = 0 to make x=3 is a


    solution ?

    a) 2 b) 4 c) 6 d) Zero

    15) After finding k value problem (14), Find the other two solutions?

    a) 𝑥 = {} b) 𝑥 = {−2, 1 } c) x={2 , -1 } d) None of above


    1 √3
    16) Find the quartic polynomial with rational coefficients has roots 1 + √5 and + 𝑖?
    2 2
    a) 𝑥 4 + 𝑥 3 − 2.5𝑥 2 + 2𝑥 − 1 = 0 b) 𝑥 4 − 3𝑥 3 − 𝑥 2 + 2𝑥 − 1 = 0
    c) 𝑥 4 − 3𝑥 3 − 𝑥 − 1 = 0 d) 𝑥 4 − 3𝑥 3 − 2.5𝑥 2 + 2𝑥 − 1 = 0
    17) Find the other roots for polynomial in eq 16 ?
    1 √3 1 √3
    a) 1 + √5 and + 𝑖 b) 1 − √5 and + 𝑖
    2 2 2 2
    1 √3 1 √3
    c) 1 + √5 and − 𝑖 d)1 − √5 and − 𝑖
    2 2 2 2

    18) What is value of k in the polynomial 𝑥 3 − 𝑘𝑥 2 + 23 𝑥 − 14 = 0 to make x=3 is a


    solution ?
    80 82
    a) b) c) 6 d) 9
    9 9

    2|Page
    Faculty of Engineering
    Basic Engineering Science. Department
    Math 1

    Theory of Equations
    19) After finding k value problem (18), Find the other two solutions?
    55 √15113 √15113
    a) 𝑥 = { ∓ } b) 𝑥 = {55 ∓ } c) 𝑥 = {0} d)𝑁one of above
    18 18 18

    20) What is value of k in the polynomial 𝑥 3 − 9𝑥 2 + 𝑘 𝑥 − 15 = 0 to make x=7 is a


    solution ?
    a) 10.25 b) 16.14 c) 6.548 d) 1.52
    21) After finding k value problem (20), Find the other two solutions?
    2 √14 √13 2 √18
    a) 𝑥 = {1 ± } b) 𝑥 = {7 ± } c) 10 ± d) None of above
    7 4 17

    22) How many possible solutions of the polynomial 𝑥 4 − 14 𝑥 3 + 64 𝑥 − 114 𝑥 +


    63 = 0 in the interval (0,14) ?

    a) 0 b) 1 c) 2 d) 4

    ➢ What are the solutions for the next Equations


    1. 6𝑥 5 + 11𝑥 4 − 33𝑥 3 − 33𝑥 2 + 11𝑥 + 6=0
    2. 2𝑥 4 + 𝑥 3 − 6𝑥 2 − 𝑥 + 2=0
    3. 3𝑥 6 + 𝑥 5 − 27𝑥 4 + 27 𝑥 − 𝑥 − 3=0

    3|Page

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