given f(x)=2x^2-4x+5, we know the roots are:a.  real, rational, and equal b. real, rational, and unequal c. real, irrational, and unequal d. imaginary AND WHY?

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justaguide eNotes educator| Certified Educator

The equation 2x^2 - 4x + 5 is of the form ax^2 + bx + c, where a = 2, b = -4 and c = 5

b^2 - 4*a*c = 16 - 40 = -24

As the determinant b^2 - 4ac is negative, the roots of the equation are imaginary.

This is because of the fact that the roots of a quadratic equation have the term sqrt (b^2 - 4ac) and the square root of a negative number is imaginary.

The roots of the equation are imaginary