JEE Advanced 2021 · Paper 1 · Mathematics Q17

MathematicsInteger+4Question 55 of 57

For $x \in \mathbb R$ , the number of real roots of the equation
$3x^2 - 4|x^2 - 1| + x - 1 = 0$
is ____.

Your answer

Answer and worked solution

Official answer: 4

Case $|x|\ge1$ . The equation becomes $-x^2+x+3=0$ , so $x=\frac{1\pm\sqrt{13}}2\approx2.30,\,-1.30$ . Both satisfy $|x|\ge1$ .

Case $|x|<1$ . The equation becomes $7x^2+x-5=0$ , so $x=\frac{-1\pm\sqrt{141}}{14}\approx0.78,\,-0.92$ . Both satisfy $|x|<1$ .

That makes 4 real roots.

JEE Advanced 2021 · Paper 1, Mathematics question 17