SOLUTION: Dear Sir/Madam, Good day! Kindly help me on this problem: Find the value of k so that the equation 3x^2-4kx+k = 0 will have real roots. Thank you very much for your help!

Algebra.Com
Question 767452: Dear Sir/Madam,
Good day! Kindly help me on this problem:
Find the value of k so that the equation 3x^2-4kx+k = 0 will have real roots. Thank you very much for your help!
Found 2 solutions by lwsshak3, solver91311:
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
Find the value of k so that the equation 3x^2-4kx+k = 0 will have real roots.
***
Equation will have 2 equal real roots when the discriminant=0
a=3, b=-4k, c=k
discriminant=b^2-4*a*c=(-4k)^2-4*3*k=16k^2-12k=0
k(16k-12)=0
k=0 (reject)
k=12/16=3/4
..
solve for x with k=3/4
3x^2-4kx+k=3x^2-3x+3/4=0
12x^2-12x+3=0
solve for x by quadratic formula:

a=12, b=-12, c=3
ans:
x=0.5 (multiplicity 2)
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Your question cannot be answered as you asked it. You cannot find the value of such that the equation has real roots. That is because the set of values of that fulfills the conditions of the problem has infinite elements.

In order for a quadratic equation, to have real roots, the discriminant, must be non-negative.





Critical points are and

Test value: -1:

Test value: 0.5:

Test value: 1:

So the intervals where values of result in real roots for the given quadratic are:



and



And a compact description of the solution set is


John

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