X square + 2 X + 3 is equal to zero

Answer: The equation has no real roots.

Step-by-step solution

Step 1: Identify coefficients

The given quadratic equation is $x^2 + 2x + 3 = 0$ . We compare this to the standard form of a quadratic equation, $ax^2 + bx + c = 0$ , to identify the coefficients $a$ , $b$ , and $c$ .

Step 2: Calculate the discriminant

The discriminant, denoted by $\Delta$ (delta), helps us determine the nature of the roots. We substitute the values of $a$ , $b$ , and $c$ into the discriminant formula.

Step 3: Substitute values and evaluate

Substituting $a=1$ , $b=2$ , and $c=3$ into the discriminant formula, we get $\Delta = (2)^2 - 4(1)(3) = 4 - 12 = -8$ .

Step 4: Interpret the discriminant

Since the discriminant $\Delta = -8$ is less than zero, the quadratic equation has no real roots. This means the roots are complex conjugates.