Question

Which of the following accurately describes the nature of the solutions to 5 x^2 - 2x + 7 = 0?
A 1 real, rational solution
B 2 real, rational solutions
C 2 real, irrational solutions
D 2 nonreal solutions

Answer 1

To find the nature of the roots, you have to use the discriminant. For \[y = ax^2 + bx + c\]the discriminant is \[\Delta = b^2 - 4ac\] If the discriminant is negative the quadratic equation has imaginary solutions. If the discriminant = 0, the equation has 1 solution. If the discriminant is positive, the equation has 2 solutions.

Answer 2

Using that information, can you answer the question?

Answer 3

Oh, also, if the discriminant is a positive perfect square, then the solutions are rational. If positive and non perfect square, than the solutions are irrational.

Answer 4

\[y = 5 x^2 - 2x + 7\]\[\Delta = (-2)^2 - 4 * 5 * 7 = -136\]Since the discriminant is negative, you have 2 imaginary solutions, Choice D.