QJEEM21Mac0d5: JEE Main 2021 Mathematics - Class 12 JEEM21Mac0d5 Solution: The number of distinct real roots of the equation 3x 4 + 4x 3…

3x⁴ + 4x³ $-$ 12x² + 4 = 0

So, let f(x) = 3x⁴ + 4x³ $-$ 12x² + 4

$\therefore$ f'(x) = 12x(x² + x $-$ 2)

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

$\therefore$ f'(x) = 12x³ + 12x² – 24x = 12x(x + 2) (x – 1)

Points of extrema are at x = 0, –2, 1

f(0) = 4

f(–2) = –28

f(1) = –1

So, 4 Real Roots