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23 November, 10:01

1) The product of a number and 1 less than the number is 42. Find the number

2) write a polynomial equation that has three solutions of 5,3, and - 8

a) x^3 - 49x + 120 = 0

b) x^3 - 120x - 49=0

c) x^3 - 49^2 + 120=0

d) x^3 - 49x - 120=0

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Answers (1)
  1. 23 November, 12:29
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    1) Answer

    One set = (7, 6)

    Second set = (-6, - 7)

    Step by step explanation

    Let "x" be a number.

    The other number = x - 1

    The product of the two number is 42

    Therefore, x (x - 1) = 42

    x^2 - x = 42

    x^2 - x - 42 = 0

    Now we have to factorize the equation.

    (x - 7) (x + 6) = 0

    x = 7 and x = - 6

    Take x = 7, and the other number = x - 1

    The number is = 7 - 1 = 6

    One set of number is (7, 6)

    The other set is when x = - 6

    The other number is = x - 1

    = - 6 - 1

    = - 7

    The other set is (-6, - 7)

    2) Answer

    a) x^3 - 49x + 120 = 0

    Step by step explanation

    Here the solution are 5, 3 and - 8

    Therefore, the factors are (x - 5) (x - 3) and (x + 8)

    Multiplying the factors we get the equation.

    (x - 5) (x - 3) (x + 8) = 0

    (x^2 - 5x - 3x + 15) (x + 8) = 0

    (x^2 - 8x + 15) (x + 8) = 0

    x^3 - 8x^2 + 15x + 8x^2 - 64x + 120 = 0

    x^3 - 49x + 120 = 0
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