Math (Quadratics)(Discriminants)

posted by .

If a is a real number and a cubic equation
f(x)=x^3−8x^2+(a+12)x−2a
has a repeated root, what is the sum of all the possible values of a?

  • Math (Quadratics)(Discriminants) -

    The repeated root cannot be complex, nor can the other.

    If f(x) = (x-h)^2 (x-k) then

    x^3 - (2h+k)x^2 + (2hk+h^2)x - kh^2 = x^3-8x^2+(a+12)x-2a

    so

    2h+k = 8
    h(2k+h) = a+12
    kh^2 = 2a

    k = 8-2h
    h(16-3h) = a+12
    h^2(4-h) = a

    h(16-3h) = h^2(4-h) + 12
    h^3 - 7h^2 + 16h - 12 = 0
    (h-2)^2 (h-3) = 0

    So,
    h = 2 or 3
    k = 4 or 2
    a = 8 or 9

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Find an equation for the surface consisting of all points P(x, y, z) equidistant from the point P(0, 1, 0) and the plane x = 3. Answer Choices: 1. y2 + z2 − 6x + 2y − 8 = 0 2. x2 + z2 + 6y − 2z − 8 = 0 3. y2 …
  2. algebra

    What is the sum of all the possible values of a for which 25x^2+(a−15)x+9 has exactly one distinct real root?
  3. math

    What is the sum of all the possible values of a for which 25x^2+(a−15)x+9 has exactly one distinct real root?
  4. math

    What is the sum of all the possible values of a for which 25x2+(a−15)x+9 has exactly one distinct real root?
  5. math

    x is a positive number such that x2+9x−22=0. What is the sum of all possible values of y which satisfy the equation x=y2−13y+24?
  6. Algebra

    If a is a real number and a cubic equation f(x)=x^3−12x^2+(a+20)x−2a has a repeated root, what is the sum of all the possible values of a ?
  7. Math (Algebra)

    If a is a real number and a cubic equation f(x) = x^3 − 8x^2 + (a+12)x − 2a has a repeated root, what is the sum of all the possible values of a?
  8. plllllls heeeeeeelp math

    Let f(x)=3^(171x−3)−3^(114x+2)+3^(57x+3)−1. Let S be the sum of all real values of x that satisfy f(x)=0. What is the value of 1/S?
  9. math

    What is the sum of all possible real values of x, such that there exists a real value y which satisfies the equation (x+y−40)^2+(x−y−18)^2=0?
  10. Calculus

    Let f be a function such that f(−6)=−6, f(6)=6, f is differentiable for all real values of x and −1≤f'x≤1 for all real values of x. Prove that f(x)=x for all −6≤x≤6 I tried applying the …

More Similar Questions