Respuesta :

Understanding Concept :-

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.

  • If Discriminant, D > 0, then roots of the equation are real and unequal.

  • If Discriminant, D = 0, then roots of the equation are real and equal.

  • If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

[tex]\quad\red{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}} [/tex]

Given Equation:-

[tex]\red{\leadsto}\: \sf{2x^2 + 4x -7= 0} [/tex]

  • α = 2
  • β = 4
  • c = -7

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.

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