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Rajan@2021
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If x³+x²-ax+b is divisible by (x²-x), write the values of a and b

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This is the basic and exam oriented question from polynomials in which we have given a polynomial x³+x²-ax+b and it is divisible by (x²-x) and we have to find the value of a and b

Kindly solve the above problem

RS Aggarwal, Class 10, chapter 2C, question no 15

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  1. It is given that the polynomial f(x)=+ax+b is divisible by x which can be rewritten as x(x1). It means that the given polynomial is divisible by both x and (x1) that is they both are factors of f(x)=+ax+b.

    Therefore, x=0 and x=1 are the zeroes of f(x) that is both f(0)=0 and f(1)=0.

    Let us first substitute x=0 in f(x)=+ax+b as follows:

    f(0)=+(a×0)+b
    0=+(a×0)+b
    0=0+b
    b=0

    Now, substitute x=1:

    f(1)=+(a×1)+b
    0=1+1a+b
    0=2a+b
    0=2a+0 (b=0)
    a=2

    Hence, a=2 and b=0.

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