Compute the discriminant. Then determine the number and type of solution for the given equation.
3x2 – 4x + 2 = 0
Solution:-
| b2– 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. |
| b2– 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. |
| b2– 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.
b2 – 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.