SOLUTION: what is the smallest integer value of k that makes the solutions of 3x^2-7x+k=0 imaginary?

Algebra ->  Real-numbers -> SOLUTION: what is the smallest integer value of k that makes the solutions of 3x^2-7x+k=0 imaginary?      Log On


   

Question 953145: what is the smallest integer value of k that makes the solutions of 3x^2-7x+k=0 imaginary?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2-7x%2Bk=0
discriminant is b%5E2-4ac
if and only if b%5E2-4ac%3C0 we have two imaginary solutions
in your case a=3,b=-7, and c=k
so, %28-7%29%5E2-4%2A3k%3C0
=>49-12k%3C0
=>49%3C12k
=>49%2F12%3Ck
=>4.083333333333333%3Ck
=>k%3E4.08
the smallest integer (whole number) value is k=5 that makes the solutions of 3x%5E2-7x%2Bk=0 imaginary