Math

find all the other zeroes of the polynomial x^4+4x^3-4x^2-32x-32 if two of its zeroes are 2 root 2 and -2 root 2

  1. 👍
  2. 👎
  3. 👁
  1. If x = 2√2 and x = -2√2
    then two of the factors are
    (x - 2√2) and (x + 2√2)
    or (x^2 - 8) must be a factor of your polynomial.

    Do a long algebraic division to get

    x^4+4x^3-4x^2-32x-32
    = (x^2 - 8)(x^2 - 4x + 4)

    we can get more roots from
    x^2 - 4x + 4 = 0
    (x-2)(x-2) = 0 ---> a perfect square
    so x = 2

    so the roots are 2 , ± 2√2

    1. 👍
    2. 👎
  2. Thank you

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. If alpha

    If alpha& beta are the zeroes of the polynomial 2x2-7x+3. Find the sum of the reciprocal of its zeroes

  3. maths

    if the zeroes of the polynomial x2-5/2x+k are reciprocal of each other, find the value of k ?

  4. Maths

    true/false 1. a cubic polynomial has at least one zero.............. 2. a quadratic polynomial an have at most two zeroes.......... 3. if r(x)is the remainder and p(x) is the divisor, then degree r(x) < degree p(x)............ 4.

  1. maths

    If one of the zeroes of the cubic polynomial x3+ax2+bx+c is -1 then the product of the other two zeroes is -------(A) b -a +1 (B) b-a-1 (C) a-b+1 (D) a-b-1

  2. Mathematics

    If zeroes of p(x)=2x²- 7x+k are reciprocal of each other, then find the value of k

  3. maths

    1. If the graph of a polynomial intersects the x – axis at three points, then the number of zeroes = _____ Q2 . The zero of the polynomial p(x) = ax +b is ______________

  4. maths

    If one of the zeroes of cubic polynomial x3 + ax2 + bx + c is - 1 then the product of the other two zeroes is -----

  1. MATH

    if alpha and beta are zeroes of the polynomial x2-5x+6,then find the polynomial whose zeroes are root 3 and -root 3

  2. math

    find the polynomial whose zeroes are -5 and -4.

  3. maths

    The number of polynomial having zeroes as -2 and 5 is --------(A) 1 (B)2 (C) 3 (D) more than 3

  4. maths

    Yash designs and builds handmade wooden furniture. He is designing a new box to have a volume of 48 cubic feet. All the boxes he built are 2 feet wider than their height and 2 feet longer than their width. a) Represent the volume

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