Identify the nature of the roots of x² − 5x + 5 = 0.

Correct answer: Two real, irrational, and distinct roots (D = 5)

The discriminant D=B²−4AC determines whether the roots are real, equal, or non-real. For x²−5x+5=0, A=1, B=−5, and C=5. Thus D=(−5)²−4(1)(5)=25−20=5. Since D>0, there are two real and distinct roots. Moreover, 5 is not a perfect square, so √5 is irrational. The quadratic formula gives x=[5±√5]/2, and both values are irrational. Therefore option A correctly combines reality, distinctness, and irrationality. Option B uses an incorrect discriminant value of 25; option C would require D=0, and option D would require D<0. Hence A is unambiguously correct.