Question

How do you find the discriminant and how many and what type of solutions does `2x^2+5x+3=0` have?

Answer 1

Your equation is in the form: `ax^2+bx+c=0`
Where:
`a=2`
`b=5`
`c=3`
The discriminant is:
`Delta=b^2-4ac=25-4(2*3)=25-24=1>0`
Now, if:
1] `Delta>0` you have 2 distinct Real solutions;
2] `Delta=0` you have two Real coincident solutions;
3] `Delta<0` you have no Real solutions.