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The polynomial fee of x is …

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The polynomial fee of x is equal to x to the power 4 - 2 x cube + 3 x square minus a x plus b when divisible by x minus 1 and x + 1 leave the remainder 5 and 19 respectively find the value of a and b

    • Posted by Furqan Azam 6 years, 3 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Gaurav Seth 6 years, 3 months ago

    Question: If f(x) = x4 - 2x3 + 3x2 - ax + b is divided by(x - 1) and (x + 1), it leaves the remainder 5 and 19 respectively. Find 'a' and 'b'.

    Answer:

    Given f(x) = x4 - 2x3 + 3x2 - ax + b

    When f(x) is divided by (x-1), it leaves a remainder 5

    f(1) = 5

     1 - 2(1)3 + 3(1)2 - a(1) + b = 5

     1 - 2 + 3 - a +b = 5

     -a + b = 3 … (i)

    When f(x) is divided by (x+1), it leaves a remainder 19

    f(-1) = 19

     (-1)4 - 2(-1)3 + 3(-1)2 - a(-1) + b = 19

    1 + 2 + 3 + a + b = 19

    a +b = 13 … (ii)

    Adding (i) and (ii),

    2b = 16  b = 8

    (i)  a = b - 3 = 8 - 3 = 5

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