Math

Q.1)If one zero of the polynomial 3x2-kx-2 is 2 find the other zero.allso find the value of k.
Q.2)If sum of the zeroes of the polynomial x2-x-k(2x-1) is 0,find the value of k
Q.3)If 2 and 3 are the zeroes of the polynomial 3x2-2kx+2m find the values of k and m
Q.4)Find the values of k so that the su of the zeros of the polynomial 3x2+(2k+1)x-k-5 is equal to the product of the zeros.
Q.5)Find the values of a and b so that x4+x3+8x2+ax+b is divisible by x2+1

  1. 👍 0
  2. 👎 0
  3. 👁 677
  1. Please type 3x^2 ... to indicate powers in this format.

    1. f(x) = 3x^2 - kx - 2
    if -2 is a "zero", then
    f(-2) = 3(4) + 2k - 2 - 0
    2k = -10
    k - -5
    so f(x) = 3x^2 + 5x - 2
    then 3x^2 + 5x - 2 = (x+2)(.......)
    by inspection
    3x^2 + 5x - 2 = (x+2)(3x - 1)
    making the other root, or zero, equal to 1/3

    2. let the zeroes be a and b
    a+b = 0 , so b = -a
    f(a) = a^2 - a - k(2a-1) = 0
    f(-a) = a^2 - (-a) - k(-2a-1) = 0
    a^2 - a - k(2a-1) = a^2 - (-a) - k(-2a-1)
    -a - 2ak + k = a + 2ak + k
    -2a -4ak = 0
    a( -2 - 4k)=0
    k =-1/2

    or (easier way)

    If the roots add up to zero, then they must be opposite, (see above)
    and the function would have to be a difference of squares.
    x^2 - x - k(2x-1)
    = x^2 - x -2kx + k
    to be a difference of squares, no x term should show up, so
    -x - 2kx = 0
    1 + 2k = 0
    k = -1/2

    3. in f(x) = 3x^2 - 2kx + 2m find
    f(2) and f(3), set those equal to 0
    You will have 2 equations in k and m, solve them.

    4. recall that for ax^2 + bx + c = 0,
    the sum of the roots is -b/a and the product of the roots is c/as
    so for 3x^2 + (2k+1)x - k-5 = 0
    let the roots be m and n
    m+n = (-2k-1)/3 and mn = (-k-5)/3

    then (-2k-1)/3 = (-k-5)/3
    -2k - 1 = -k - 5
    k=4

    5. see next post

    1. 👍 0
    2. 👎 0
  2. 5. if x^2 + 1 is a factor then x = ± i are roots,
    remember that i^1 - -1 and i^4 = +1

    f(i) = 1 - i - 8 - ai + b = 0
    f(-i) = 1 + i -8 + ai + b = 0
    add them
    2 - 16 + 2b = 0
    b = 7
    so the function is
    f(x) = x^4 + x^3 + 8x^2 + ax + 7

    I then did a long division of that function by x^2 + 1.
    This left me with a remainder of x(a-1), but there shouldn't have been a remainder, so
    x(a-1) = 0
    so a = 1

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Write and simplify the polynomial represented by the model. polynomial blocks A. –2x2 + 2x + 3 B. 2x2 – 2x – 3 C. 3x2 – 2x – 3 D. 2x2 – 2x + 3

    asked by anonymous on May 22, 2019
  2. Math

    Consider the polynomial f(x) = 2x^3 – 3x^2 – 8x – 3. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work,

    asked by Carmin on July 22, 2009
  3. Algebra 2

    1) Find the roots of the polynomial equation. x^3-2x^2+10x+136=0 2) Use the rational root theorem to list all problem rational roots of the polynomial equation. x^3+x^2-7x-4=0. Do not find the actual roots.

    asked by Anonymous on December 4, 2017
  4. College Alg

    Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer correct to two decimal places. (If an answer does not exist, enter DNE.) y = 2x3 − 3x2 − 12x − 32, [ −5, 5]

    asked by miriam on July 22, 2015
  5. Math help please ASAP

    2. Simplify the polynomial. –3f^2 + 4f – 3 + 8f^2 + 7f + 1 5f^2 – 11f + 2 11f^2 + 11f + 2 5f^2 + 11f – 2 –5f^2 + 11f – 2 3. (2x2 + 6x + 1) + (–7x2 + 2x – 3) 5x2 – 4x – 2 –5x2 + 8x – 2 5x2 – 8x + 2 –9x2

    asked by Delilah on May 6, 2013
  1. algebra 2

    3x2 – 12x + 7x – 28 factor the polynomial by grouping

    asked by hannah on October 22, 2013
  2. Algebra

    Can someone please explain how to do these problems. 1)write a polynomial function of least degree with intregal coefficients whose zeros include 4 and 2i. 2)list all of the possible rational zeros of f(x)= 3x^3-2x^2+7x+6. 3)Find

    asked by Marissa on August 10, 2007
  3. Math

    Find a polynomial p of degree 3 so that p(4) = 5, p(−1) = 5, p(−3) = −37, p(2) = −7, then use your polynomial to approximate p(1). p(x) = 0 p(1) = 0

    asked by Excel on October 11, 2015
  4. Rational Zeros

    List all possible rational zeros for the polynomial below. Find all real zeros of the polynomial and factor f(x)=2x^4+19x^3+37x^2-55x-75

    asked by JB on January 2, 2012
  5. algrbra 2

    Find the value of the polynomial when x = 4. 4x3 - 3x2 - 3x + 2

    asked by SArA on October 16, 2009

You can view more similar questions or ask a new question.