The number of distinct real roots of the equation 3 x 4 + 4 x 3 - 12 x 2 + 4 = 0 is _________.

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The number of distinct real roots of the equation

3 x^{4} + 4 x^{3} - 12 x^{2} + 4 = 0

is _________.

MathematicsApplication of DerivativesJEE MainJEE Main 2021 (27 Aug Shift 1)

Solution:

1772 Upvotes Verified Answer

The correct answer is: 4

$3 x^{4} + 4 x^{3} - 12 x^{2} + 4 = 0$

So,

let $f (x) = 3 x^{4} + 4 x^{3} - 12 x^{2} + 4$

$∴ f^{'} (x) = 12 x (x^{2} + x - 2)$

$= 12 x (x + 2) (x - 1)$

$f (0) = 4$

$f (1) = - 1$

Ans. $4$

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