Final answer:
To find the difference between the roots (alpha-beta) of the given quadratic equation 2x^2-3x+4=0, we use the identity α-β = √(b^2-4ac)/a. The roots are complex, as the discriminant is negative, meaning α-β represents the difference in the imaginary parts of the roots.
Step-by-step explanation:
The equation 2x^2-3x+4=0 is a quadratic equation where alpha (α) and beta (β) represent the roots. To find the difference between the roots, alpha-beta (α-β), we can use the identity α-β = √(b^2-4ac)/(a), which is derived from the quadratic formula.
In this case, the coefficients are a=2, b=-3, and c=4. Plugging these into the identity gives:
α-β = √((-3)^2-4(2)(4))/(2)
α-β = √(9-32)/2
α-β = √(-23)/2
Since the discriminant b^2-4ac is negative, the roots are complex and not real numbers. This means that alpha-beta (α-β) is also a complex number, and it represents the difference in their imaginary parts.