Problem 1086

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.

 

 

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