NCERT · Class 10 · Mathematics · Quadratic EquationsWrite the nature of roots of the quadratic equation 3x² - 4x + 5 = 0 without solving it.

To determine the nature of the roots of the quadratic equation 3x² - 4x + 5 = 0 without fully solving it, we calculate its discriminant D = b² - 4ac. Comparing with the standard form, we get a = 3, b = -4, and c = 5. Substituting these values gives D = (-4)² - 4(3)(5), which equals 16 - 60, resulting in D = -44. Since the discriminant is less than zero, the equation has no real roots and possesses two complex conjugate roots.