10 coins to best answer given the equation 2x^2 - 5x + 7 = 0. find the discriminant. describe the roots and explain your reasoning.

For quadratic
.. ax^2 +bx +c = 0
the discriminant is
.. d = b^2 -4ac

You have
.. a = 2
.. b = -5
.. c = 7
so the value of the discriminant for your equation is
.. (-5)^2 -4(2)(7)
.. = 25 -56
.. = -31

Because the discriminant is negative, the roots of the quadratic are complex.

Reasoning: this is the usual interpretation of the sign of the discriminant. It derives from the fact that the square root of the discriminant is part of the roots of the quadratic. That part will be imaginary when the discriminant is negative.

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The graph shows there are no real roots.