Let us consider a quadratic equation αx² + βx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.
Where,
[tex]\quad\red{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}} [/tex]
[tex]\red{\leadsto}\: \sf{2x^2 + 4x -7= 0} [/tex]
Now,
[tex]\quad\green{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}} [/tex]
[tex]\begin{gathered}\begin{gathered}\implies\quad \sf D = 4^2-4\times 2\times ( - 7) \end{gathered} \end{gathered} [/tex]
[tex]\begin{gathered}\begin{gathered}\implies\quad \sf D = 16-( - 56)\end{gathered} \end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf D = 16 + 56\end{gathered}[/tex]
[tex]\begin{gathered}\begin{gathered}\implies\quad \sf D = 72 \end{gathered} \end{gathered} [/tex]
Since, Discriminant, D > 0, then roots of the equation are real and distinct.