6. If x – 2 is a factor of x²+ ax + b and a + b = 1, find the values of a and b​

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6. If x – 2 is a factor of x²+ ax + b and a + b = 1, find the values of a and b​

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Delilah 2 months 2021-12-03T05:35:09+00:00 1 Answer 0 views 0

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    2021-12-03T05:37:06+00:00

     Let \: p(x) = x^{2} + ax + b

     If \: (x-2) \: is \:a \: factor \: of \: x^{2} + ax + b

     then \: p(2) = 0

     \implies 2^{2} + a\times 2 + b = 0

     \implies 4 + 2a + b = 0 \: ---(1)

     and \: a + b = 1 \: ---(2) \: (given)

    /* subtract equation (2) from equation (1) , we get*/

     \implies 4 + a = -1

     \implies a = -1 - 4

     \implies a = -5

    Put \: a = -5 \: in \: equation \:(2), we \:get

    \implies -5 + b = 1

    \implies  b = 1 + 5

    \implies  b = 6

    Therefore.,

     \green { a = -5 , \: and \: b = 6 }

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