SOLUTION: Please help me solve this problem prove that for all values ok k ,roots of this equation ( x^2-2((k)+(1/k))x+3=0) are real

Question 773965: Please help me solve this problem
prove that
for all values ok k ,roots of this equation ( x^2-2((k)+(1/k))x+3=0) are real
Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
x^2-2((k)+(1/k))x+3=0
discriminant = d = (-2((k)+(1/k)))^2-4(1)(3) =
4(k^2+2+1/k^^2) -12
= 4k^2+8+4/k^2 -12
= 4k^2+4/k^2 -4
= 4(k^2+1/k^2 -1)
= 4 ((k-1/k)^2 +1) >0
Then the equation has 2 real solutions

I can help you with more questions at: mthman@gmail.com
Thanks
RELATED QUESTIONS
Please help me answer this: Show, without solving the equation, that the roots of... (answered by josgarithmetic)

Please help me answer this: For what values of k will the equation 3x^2=k-2x have real... (answered by MathLover1)

could someone assist me on how i can crack this problem it says in the quadratic equation (answered by Theo)

Please help me with this problem: The figure shows the graph of the polynomial function... (answered by jake_6233)

show that x^2+(3k-2)x+k(k-1)=0 has real roots for all value of... (answered by fcabanski)

f(x) = x^3 + (1 - k^2)x + k (a) Show that -k is a root of f. I've already solved this (answered by jsmallt9)

Please help me solve this question: For what value of k does x^2 + kx + 1 = 0 have two (answered by ikleyn)

What are the values o k which will give 4x^2+(k+7)x+(k+4)=0 equal,real roots? Please help (answered by ilana)

Could you please help me with this? The roots of the equation (x � 1)(x + k) = -4 are... (answered by josgarithmetic)