To find the value of a, we'll use the quadratic formula to solve for the roots. The quadratic formula is as follows:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
However, we know one root of the equation is 1, so we can substitute this into the equation to solve for 'a':
1 = [-a ± sqrt(a^2 - 4*2*3)] / 2*2
This simplifies further to:
1 = [-a ± sqrt(a^2 - 24)] / 4
To rearrange the equation and isolate 'a', we multiply both sides by 4:
4 = -a ± sqrt(a^2 - 24)
Subtract 4 from both sides:
a = -4 ± sqrt(16 - 24)
This results in the solutions:
a = -4 +/- sqrt(-8)
However, the square root of -8 is not a real number. We can conclude that there has been a mistake in the equation or the statement of the problem.
As such, none of the provided options (A) 2, B) 3, C) -1, or D) -3 can be the correct answer.