Answer:
Two complex (imaginary) solutions.
Step-by-step explanation:
To determine the number/type of solutions for a quadratic, we can evaluate its discriminant.
The discriminant formula for a quadratic in standard form is:
[tex]\Delta=b^2-4ac[/tex]
We have:
[tex]3x^2+7x+5[/tex]
Hence, a=3; b=7; and c=5.
Substitute the values into our formula and evaluate. Therefore:
[tex]\Delta=(7)^2-4(3)(5) \\ =49-60\\=-11[/tex]
Hence, the result is a negative value.
If:
- The discriminant is negative, there are two, complex (imaginary) roots.
- The discriminant is 0, there is exactly one real root.
- The discriminant is positive, there are two, real roots.
Since our discriminant is negative, this means that for our equation, there exists two complex (imaginary) solutions.
