8. If a +c+e=0 and b+d=0, then find the zeroes of the polynomial ax⁴+ bx³ + cx² + dx +e. ​

Question

8. If a +c+e=0 and b+d=0, then find the zeroes of the polynomial
ax⁴+ bx³ + cx² + dx +e.

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Allison 1 month 2021-08-20T19:52:13+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-20T19:53:55+00:00

    Answer:

    Given, a+c+e=0 and b+d=0

    ⇒c=–(a+e) and d=–b

    Now, ax

    4

    +bx

    3

    +cx

    2

    +dx+e

    =ax

    4

    +bx

    3

    +[–(a+e)]x

    2

    +(–b)x+e

    =ax

    4

    –ax

    2

    –ex

    2

    +e+bx

    3

    –bx

    =ax

    2

    (x

    2

    –1)–e(x

    2

    –1)+bx(x

    2

    −1)

    =(x

    2

    −1)(ax

    2

    –e+bx)

    =(x+1)(x–1)(ax

    2

    –e+bx) ……….(1)

    As (x+1) and (x–1), are the factors of (1)

    so, it is divisible by both (x+1) and (x–1)

    Hence the zeroes are −1,1 and x=

    2a

    −b±

    b

    2

    +4ae

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