6 hwork 1.3

Question

Determine
k
so that the following has exactly one real solution. (Enter only the positive answer.)

5x^2+kx+3=0

Answer 1

To ensure there is only one real solution, you need to make the discriminant equal to zero.

 

D = b² - 4ac = k² - 4*5*3 = k² - 60 = 0 ⇒ k = √60 = 2√15

 

 

Answer 2

For there to be exactly one solution of a quadratic, the discriminant must be 0.

b² - 4ac will be, in this case, k² - 4(5)(3) = 0   so   k must be √60.