SOLUTION: The quadratic equation {{{6x^2+hx+k=0}}} has roots {{{x}}} and {{{1/x}}}/ Find a. The value of {{{k}}}, b. the values of {{{h}}} given that {{{x^2+1/x^2=-7/4}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The quadratic equation {{{6x^2+hx+k=0}}} has roots {{{x}}} and {{{1/x}}}/ Find a. The value of {{{k}}}, b. the values of {{{h}}} given that {{{x^2+1/x^2=-7/4}}}      Log On


   

Question 704741: The quadratic equation 6x%5E2%2Bhx%2Bk=0 has roots x and 1%2Fx/ Find
a. The value of k,
b. the values of h given that x%5E2%2B1%2Fx%5E2=-7%2F4
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The quadratic equation 6x^2 + hx + k = 0 has roots x and x and 1/x Find:
:
Use the coefficient of x^2 to derive the factors that satisfy this requirement:
(6x+1)(x+6) FOILs to: 6x^2 + 36x + x + 6 = 6x^2 + 37x + 6
Roots: -1/6, -6
:
a. The value of k, 6
:
b. the values of h given that x%5E2+%2B+%281%2Fx%5E2%29+=+-7%2F4
multiply by 4x^2, resulting in:
4x^4 + 4 = -7x^2
4x^4 + 7x^2 + 4 = 0
h = 7