Find the discriminant of the quadratic equation $2x^2 - 4x + 3 = 0$, and hence find the nature of its roots.
Step-by-Step Solution
Key Concept: Calculate $D = b^2 - 4ac$. If $D < 0$, roots are not real.
Stepwise Solution:
Here $a=2, b=-4, c=3$. $D = (-4)^2 - 4(2)(3) = 16 - 24 = -8$. [1.0 Mark]
Since $D = -8 < 0$, the given quadratic equation has no real roots (or imaginary roots). [1.0 Mark]
Marking Scheme:
• Calculating $D = -8$: 1.0 Mark
• Stating nature of roots (no real roots): 1.0 Mark
Correct Answer: