Question

What will be the nature of roots of quadratic equation 2x²+4x-7=0?
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Answer 1

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,

`\quad\red{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}}`

Given Equation:-

`\red{\leadsto}\: \sf{2x^2 + 4x -7= 0}`

• α = 2
• β = 4
• c = -7

Now,

`\quad\green{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}}`

`\begin{gathered}\begin{gathered}\implies\quad \sf D = 4^2-4* 2* ( - 7) \end{gathered} \end{gathered}`

`\begin{gathered}\begin{gathered}\implies\quad \sf D = 16-( - 56)\end{gathered} \end{gathered}`

`\begin{gathered}\implies\quad \sf D = 16 + 56\end{gathered}`

`\begin{gathered}\begin{gathered}\implies\quad \sf D = 72 \end{gathered} \end{gathered}`

Since, Discriminant, D > 0, then roots of the equation are real and distinct.