Which of the following equation has imaginary roots?

x² + 4x + 1 = 0

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2x² + 5x + 3 = 0

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3x² + 7x + 9

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x² + 2√2 x + 1

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Solution

The correct option is C
3x² + 7x + 9

Find discriminant for the equation.
(A) $△ = 16 - 4$ x $1 > 0$
$\Rightarrow$ real roots
(B) $△ = 25 - 4$ x $2$ x $3 >$ 0
$\Rightarrow$ real roots
(C) $3 x^{2} + 7 x + 9 = 0$
$△ 7^{2} - 4$ x $3$ x $9 < 0$
$\Rightarrow$ Imaginary roots
(D) $x^{2} + 2 \sqrt{2} x + 1$
$△ = (2 \sqrt{2})^{2} - 4$ x $1 > 0$
$\Rightarrow$ real roots

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1 :

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