x2-2x+3=0

Without solving the equation, determine the number of solutions. show all work.

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x^2-2x+3 = 0.

To solve the equation and assess the roots.

Solution:

The quadratic ax^2+bx+c = 0 has the discriminant D = b^2-4ac. If b^2-4ac is negative then the quadratic has two distinct imaginary roots.

In the given case, the discriminant is (-2)^2-4*1*3 = 4-12 = -8. So the discriminant is negative. Therefore this quadratic equation has no real roots. But it has two distinct imaginary roots.

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