Number of real roots of equation $2 x^{99} + 3 x^{98} + 2 x^{97} + 3 x^{96} + . . . . . . . . + 2 x + 3 = 0$ are

99

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49

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1

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3

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Solution

The correct option is D $1$
$2 x^{99} + 3 x^{98} + 2 x^{97} + 3 x^{96} + . . . . . . . . + 2 x + 3 = 0$ .... $(i)$
Taking $2 x + 3$ common, we get
$(2 x + 3) (x^{98} + x^{97} + . . .1) = 0$
Since $x^{98} + x^{97} + . . .1$ can not be equal to zero
Therefore only $2 x + 3 = 0$ or $x = - \frac{3}{2}$ is real root
Hence, number of real roots of equation $(i)$ is $1$ .

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