Algebra II

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Given f(x)=x^3-7x^2+6x+14, what is the

a. sum of its zeros?
b. product of its zeros?
c. sum of the squares of its zeros?

  • Algebra II -

    This is a cubic equation, so there are three roots (real/complex).
    If a,b,c represent the three zeroes, and if the left-hand-side is factorizable, then it factorizes into:
    (x-a)(x-b)(x-c) which expands to
    x³-(a+b+c)x²+(ab+bc+ca)x-abc..(1)
    The sum and product of the roots can be read off readily from the above equation (1).

    Hint for the sum of squares of the roots:
    Consider: The sum of squares of the roots represent:
    (a+b+c)²
    =(a²+b²+c²) + 2(ab+bc+ca)

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