The quadratic equation is:
[tex]y=2x^2+5x+10[/tex]To find if the number of solutions, we use the discriminant of the equation. But first, we compare the given equation with the general quadratic equation:
[tex]y=ax^2+bx+c[/tex]By comparison, we find the values of a, b, and c:
[tex]\begin{gathered} a=2 \\ b=5 \\ c=10 \end{gathered}[/tex]Now, as we said previously, we have to use the discriminant to find the number of solutions. The discriminant is defined as follows:
[tex]D=b^2-4ac[/tex]• If the value of D results to be equal to 0, there will be 1 real solution.
• If the value of D results to be greater than 0, there will be 2 real solutions.
• And if the value of D results to be less than 0, there will be no real solutions.
We substitute a, b and c into the discriminant formula:
[tex]D=5^2-4(2)(10)[/tex]Solving the operations:
[tex]\begin{gathered} D=25-4(2)(10) \\ D=25-80 \\ D=-55 \end{gathered}[/tex]As we can see, the value of D is less than 0 (D<0) which indicates that there will be no real solutions for this quadratic equation.
Answer: No real solutions
