Question 948573: Please help me answer this: For what values of k will the equation 3x^2=k-2x have real roots?
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! 
 =>  ,  , and 
The argument of the square root, the expression  , is called the "discriminant" because, by using its value, you can discriminate between (tell the differences between) the various solution types.
if  there is no real roots
if  there is one real roots
if  there are two real roots
so, we need
if there is one real roots
if there are two real roots
and I will write both in one as 
now just plug in , , and
so, if  we will have one real root which is  (you can check it)
if , using for example  we will have two real roots which are  and 
so, to get real root/roots, you can use any value for  from [ , )
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