For which values of k will x^3-x^2-8x+k=0 have three real roots

1 answer

Let f(x)=x^3-x^2-8x=x(x^2-x-8).
f(x) has 3 real roots.
f'(x)=3x^2-2x-8=(3x+4)(x-2)
maxf(x)=f(-4/3)=-64/27-16/9+32/3=176/27
minf(x)=f(2)=8-4-16=-12

-176/27<k<12
Similar Questions
  1. Which correctlydescribes the roots of the following cubic equation? x3 - 3x2 + 4x - 12 = 0 (1 point) Three real roots, • each
    1. answers icon 1 answer
  2. Which correctly describes the roots of the following cubic equation?x^3 - 3x^2 + 4x - 12 = 0 a. Three real roots, each with a
    1. answers icon 1 answer
  3. Which correctly describes the roots of the following cubic equation??x^3 - 3x^2 + 4x - 12 = 0 a. Three real roots, each with a
    1. answers icon 1 answer
  4. determine the values of k for which the quadratic equation x^2=kx+9=oa) 2 equal real roots b) 2 distinct real roots can i get
    1. answers icon 2 answers
more similar questions