Q2. If a,ß are the zeroes of p(x)= x²-5x+ b and a-b=1, then b is​

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Q2. If a,ß are the zeroes of p(x)= x²-5x+ b and a-b=1, then b is​

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Quinn 4 weeks 2021-08-16T12:28:32+00:00 1 Answer 0 views 0

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    2021-08-16T12:30:20+00:00

    Answer:

    b = 1 +  \sqrt{5}  \: or \: 1 -  \sqrt{5}

    Explaination

    The given polynomial is

    p(x) =  {x}^{2}  - 5x + b

    Since ‘a’ is a zero of the polynomial, p(a) = 0

     {a}^{2}  - 5a + b = 0..........(1)

    It is also given that

    a - b = 1 \: or \: b = a - 1

    Substituting this in (1) we get

     {a}^{2}  - 5a + a - 1 = 0

     {a}^{2}  - 4a - 1 = 0

    a =  \frac{4 +  -  \sqrt{ {4}^{2} - 4.1.( - 1)}  }{2 \times 1}

    a =  \frac{4 +  -  \sqrt{20} }{2}

    a = \frac{4 +  - 2 \sqrt{5} }{2}

    a = 2 +  -  \sqrt{5}

    Now

    b = a - 1 = (2 +  -  \sqrt{5} ) - 1

    b = 1 +  -  \sqrt{5}

    b = 1 +  \sqrt{5}  \: or \: 1 -  \sqrt{5}

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