Find the discriminant of the quadratic equation 2x2−4x+3=0, and hence find the nature of its roots.
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Step-by-Step Solution
Step 1: Identify coefficients
We compare the given quadratic equation 2x2−4x+3=0 with 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 D (or Δ), is calculated using the formula D=b2−4ac. This value determines the nature of the roots of the quadratic equation.
Step 3: Substitute and evaluate
Substitute the values of a=2, b=−4, and c=3 into the discriminant formula. First, calculate the square of b, then the product of 4ac, and finally subtract the two results to find the value of D.
Step 4: Determine the nature of roots
Since the calculated discriminant D=−8 is less than zero (D<0), the quadratic equation has no real roots. This means the roots are complex or imaginary.