Question

Find the discriminant of the quadratic equation
2x + x + 4 = 0, hence
find the nature of its roots.
find the nature of its roots​

Answer 1

$\textbf{\underline {\underline {Solution:}}}$

$d = {b}^{2} - 4ac \\ \: \: {1}^{2} - 4 \times 2 \times 4 \\ D= - 32$

$\textbf{\underline{D<0 Then there is no Roots }}$

Answer 2

$\huge{\mathfrak{\underline{\underline \red{ Correct \: Question-}}}}$

•find the discriminant and nature of given equation – $\large\sf\ 2x^2 \: + \: x \: + \: 4$

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$\huge{\mathfrak{\underline{\underline \red{Answer-}}}}$

★Ｇｉｖｅｎ-

A quadratic equation → $\sf\ 2x^{2} \: + \: x \: + \: 4$

★ Ｔｏ ｆｉｎｄ-

⠀⠀• The discriminant

⠀⠀• Nature of roots

★Ｓｏｌｕｔｉｏｎ-

$\large\sf\ Formula \: to \: find \: discriminant \: -$

${\boxed{\sf\orange{D \: = \: b^{2} \: - \: 4ac}}}$

From equation ;

⠀⠀⠀• a → 2

⠀⠀⠀• b → 1

⠀⠀⠀• c → 4

Now,consitute it accordingly ;

$\large\to\sf\ D \: = \: (1)^2 \: - \: 4 \times\ 2 \times\ 4 \\ \\ \large\to\sf\ D \: = \: 1 \: - 32 \\ \\ \large\to\sf\ D \: = \: -31$

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★ Ｔｈｅｒｅｆｏｒｅ–⠀⠀⠀

$\large\bullet\sf\ Value \: of \: D \: = \: -31 \\ \\ \large\bullet\sf\ Nature \: of \: roots \: = \: Ｎon-real \: roots$(As value of D is smaller than 0)

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