According to the discriminant of the quadratic equation, it is found that 6x^2 - 2X + 7 = 0 has 2 no real solutions.
What is the discriminant of a quadratic equation and how does it influence the solutions?
A quadratic equation is modeled by:
\(y = ax^2 + bx + c\)
The discriminant is:
\(\Delta = b^2 - 4ac\)
The solutions are as follows:
- If \(\mathbf{\Delta > 0}\), and it is a perfect square, it has 2 rational solutions.
- If \(\mathbf{\Delta > 0}\), and it is not a perfect square, it has 2 irrational solutions.
- If \(\mathbf{\Delta = 0}\), it has 1 rational solutions.
- If \(\mathbf{\Delta < 0}\), it has 2 complex solutions.
In this problem, the equation is:
\(6x^2 - 2x + 7 = 0\)
Hence the coefficients are a = 6, b = -2, c = 7 and the discriminant is given by:
\(\Delta = (-2)^2 - 4(6)(7) = -164\)
Negative discriminant, hence the correct option is 2 no real solutions.
More can be learned about quadratic equations at https://brainly.com/question/19776811
