JEE MAIN - Mathematics (2021 - 27th August Morning Shift - No. 13)
The number of distinct real roots of the equation 3x4 + 4x3 $$-$$ 12x2 + 4 = 0 is _____________.
Answer
4
Explanation
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
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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
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