Compute the discriminant. Then determine the number and type of solution for the given equation.

3x^{2} – 4x + 2 = 0

**Solution:-**

b^{2}– 4ac > 0 |
Two unequal real solutions; if a, b, and c are rational numbers and the discriminant is a perfect square, the solution are rational. If the discriminant is not a perfect square, the solution are irrational. |

b^{2}– 4ac = 0 |
One solution (a repeated solution) that is a real number; if a, b, and c are rational number, the repeated solution is also a rational number. |

b^{2}– 4ac < 0 |
No real solution; two complex imaginary solution; The solution are complex conjugates. |

Using a = 3, b = -4, and c = 2, we evaluate the discriminate.

b^{2} – 4ac = (-4)^{2} – 4 (3)(2) = -8

since b – 4ac < 0 there is no real solution to the quadratic equation. The solutions are complex conjugates.