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