help me with this

Question

Determine the nature of the solutions to the equation: 10 - 3x2 = 6x - 14



A. Two irrational, real solutions
B. Two complex solutions that are not real
C. One repeated, real solution
D. Two rational, real solutions

 which one is it? im confused

Answer 1

First, express this as a quadratic equation in standard form, then evaluate the discriminant.

 

10 - 3x² = 6x - 14

 

3x² + 6x - 24 = 0

 

D = b² - 4ac = 6² - 4(3)(-24) = 324 > 0 ⇒ two real solutions

 

D = 324 = 18² = a perfect square, so the solutions are also rational

 

Answer: Two real and rational solutions