X square + 2 X + 3 is equal to zero
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Step-by-Step Solution
Step 1: Identify coefficients
The given quadratic equation is x2+2x+3=0. We compare this to the standard form of a quadratic equation, ax2+bx+c=0, to identify the coefficients a, b, and c.
Step 2: Calculate the discriminant
The discriminant, denoted by Δ (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 Δ=(2)2−4(1)(3)=4−12=−8.
Step 4: Interpret the discriminant
Since the discriminant Δ=−8 is less than zero, the quadratic equation has no real roots. This means the roots are complex conjugates.