SOLUTION: Show that the equation {{{ (9k-8)x^2-6kx+k+2=0 }}} has roots which are different if {{{ k<8/5 }}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Show that the equation {{{ (9k-8)x^2-6kx+k+2=0 }}} has roots which are different if {{{ k<8/5 }}}      Log On


   

Question 1134883: Show that the equation +%289k-8%29x%5E2-6kx%2Bk%2B2=0+ has roots which are different if +k%3C8%2F5+
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Show that the equation +%289k-8%29x%5E2-6kx%2Bk%2B2=0+ has roots which are different if +k%3C8%2F5+
discriminant b%5E2-4ac+shows you when equation has 2 different roots
if you want distinct real roots, therefore the discriminant must be positive:
b%5E2-4ac+%3E0
in your case a=%289k-8%29, b=6k, and c=k%2B2
so, %286k%29%5E2-4%289k-8%29%28k%2B2%29+%3E0
36k%5E2-%2836k-32%29%28k%2B2%29+%3E0
36k%5E2-%2836+k%5E2+%2B+40+k+-+64%29+%3E0
36k%5E2-36k%5E2+-40k+%2B64+%3E0
+-40k+%2B64+%3E0
+64+%3E40k
k%3C64%2F40
k%3C8%2F5