We are asked to find out which of the given quadratic equation has no real solutions.
Recall that a quadratic equation has no real solutions if the discriminant is less than 0.
The discriminant is given by
[tex]d=b^2-4ac[/tex]
Where a, b, and c are the coefficients of the quadratic equation.
Let us analyze each of the given quadratic equations.
Option A:
[tex]2x^2+2x+15=0[/tex]
The coefficients are
a = 2
b = 2
c = 15
The discriminant is
[tex]\begin{gathered} d=b^2-4ac \\ d=2^2-4(2)(15) \\ d=4-120 \\ d=-116 \end{gathered}[/tex]
As you can see, the discriminant is less than 0, therefore, this quadratic equation has no real solutions.
Therefore, the correct answer is option A.
