If $(2 x^{2} - 3 x + 1) (2 x^{2} + 5 x + 1) = 9 x^{2}$

For real root

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Two real and two imaginary root

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Four imaginary roots

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None of the above

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Solution

The correct option is A For real root
$(2 x^{2} - 3 x + 1) (2 x^{2} + 5 x + 1) = 9 x^{2}$
$⟹ 4 x^{4} + 10 x^{3} + 2 x^{2} - 6 x^{3} - 15 x^{2} - 3 x + 2 x^{2} + 5 x + 1 = 9 x^{2}$
$⟹ 4 x^{4} + 4 x^{3} - 2 x^{2} + 2 x + 1 = 0$
$∴$ Real Root

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