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AnilSinghBora
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If the zeroes of the polynomial x3-3×2+x+1 are a – b, a, a + b, find a and b.Q.3

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This is also an important question of class 10th. Please help me for solving this question. This optional exercise also an important exercise of class 10th. How i solve easily please help me for this question If the zeroes of the polynomial x3-3×2+x+1 are a – b, a, a + b, find a and b

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  1. We are given with the polynomial here,

    p(x) = x3-3x2+x+1

    And zeroes are given as a – b, a, a + b

    Now, comparing the given polynomial with general expression, we get;

    ∴px3+qx2+rx+s = x3-3x2+x+1

    p = 1, q = -3, r = 1 and s = 1

    Sum of zeroes = a – b + a + a + b

    -q/p = 3a

    Putting the values q and p.

    -(-3)/1 = 3a

    a=1

    Thus, the zeroes are 1-b, 1, 1+b.

    Now, product of zeroes = 1(1-b)(1+b)

    -s/p = 1-b2

    -1/1 = 1-b2

    b2 = 1+1 = 2

    b = √2

    Hence,1-√2, 1 ,1+√2 are the zeroes of x3-3x2+x+1.

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