Question

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

Answer 1

`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`