Question

Find the solutions of the quadratic equation 3x2 - 4x + 4 = 0

Answer 1

No real solution

Explanation:

`3x^2-4x+4=0\quad\implies\quad a=3\,,\quad b=-4\,,\quad c=4\\\\\\x=(-b\pm√(b^2-4ac))/(2a)\\\\x=(-(-4)\pm√((-4)^2-4\cdot3\cdot4))/(2\cdot3)=(4\pm√(-32))/(6)`

There is no solution in real number as it's no real √[-32]

{solutins in complex numbers would be:
`x_1=(4+4√(2)\,i)/(6)=(2+2√(2)\,i)/(3)\\ x_2=(2-2√(2)\,i)/(3)` }