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If a, b and c are the roots of x3 - 6x2 + 11x - 6 = 0 then, find the value of [(4 - a)(4 - b)(4 - c)].
    Correct answer is '6'. Can you explain this answer?
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    If a, b and c are the roots of x3 - 6x2 + 11x - 6 = 0 then, find the v...
    If a, b, c are the roots of x3 - 6x2 + 11x - 6 = 0 means that,
    ► (x - a)(x - b)(x - c) = x3 - 6x2 + 11x - 6---(i)
    Substituting x = 4 in (i), we get,
    ► (4 - a)(4 - b)(4 - c) = 43 - 6 x 42 + 11 x 4 - 6 = 6
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    Community Answer
    If a, b and c are the roots of x3 - 6x2 + 11x - 6 = 0 then, find the v...
    The expression [(4-a)(4-b)(4-c)] can be simplified as:
    [(4-a)(4-b)(4-c)]
    = 64 - 16(a+b+c) + 4(ab+bc+ac) - abc

    For a cubic equation ax^3 + bx^2 + cx + d = 0 with roots x1, x2 and x3,
    x1 + x2 + x3 = -(Coefficient of x^2/ Coefficient of x^3) = -(b/a)
    (x1)(x2) + (x2)(x3) + (x1)(x3) = Coefficient of x/ Coefficient of x^3 = c/a
    (x1)(x2)(x3) = -(Constant/ Coefficient of x^3) = -(d/a)

    Hence, fetching these values from the given expression and utilizing them in the simplified expression, we get:
    [(4-a)(4-b)(4-c)]
    = 64 - 16(a+b+c) + 4(ab+bc+ac) - abc
    = 64 - 16(6) + 4(11) - (-6)
    = 64 - 96 + 44 + 6
    = 108 - 102 = 6

    Hence, the solution to the question is 6.
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    If a, b and c are the roots of x3 - 6x2 + 11x - 6 = 0 then, find the value of [(4 - a)(4 - b)(4 - c)].Correct answer is '6'. Can you explain this answer?
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