What is the nature of the roots of the quadratic equation x2 - 5x + 7 = 0?

Explanation

To determine the nature of the roots of the quadratic equation: x2 - 5x + 7 = 0 we use the discriminant. For a quadratic equation of the form ax2 + bx + c = 0, the discriminant D is given by: D = b2 - 4ac Given Values a=1 b = -5 c=7 Step 1: Calculate the Discriminant Substitute the values of a, b, and c into the discriminant formula: D = (-5)2 - 4 × 1 × 7 D = 25 - 28 D = -3 Step 2: Determine the Nature of the Roots The nature of the roots depends on the value of the discriminant D: If D > 0, the roots are real and distinct. If D = 0, the roots are real and equal. If D < 0, the roots are complex (non-real). Since D = -3, which is less than zero, the roots of the equation are complex (non- real). Final Answer The roots of the quadratic equation x2 - 5x + 7 = 0 are complex (non-real).