What is the discriminent and the solutions of 2x^2+3x+5?

1 Answer
Mar 7, 2018

x=-3/4+-sqrt(31)/4 i

Explanation:

color(blue)("Determining the discriminant")

Consider the structure y=ax^2+bx+c

where x=(-b+-sqrt(b^2-4ac))/(2a)

The discriminant is the part b^2-4ac

So in this case we have:

a=2; b=3 and c=5

Thus the discriminant part b^2-4ac -> (3)^2-4(2)(5) =-31

As this is negative it means that the solution to ax^2+bx+c is such that x is not in the set of Real Numbers but is in the set of Complex numbers.
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color(blue)("Determine the solution for "ax^2+bx+c=0)

#Using the above formula we have:

x=(-3+-sqrt(-31))/4

x=-3/4+-sqrt(31xx(-1))/4

x=-3/4+-sqrt(31)/4 i