List of top Mathematics Questions on Theory of Equations asked in JEE Main

Let $f$ be a function such that $3f(x)+2f\!\left(\dfrac{m}{19x}\right)=5x$, $x\ne0$, where $m=\displaystyle\sum_{i=1}^{9} i^2$. Then $f(5)-f(2)$ is equal to
The smallest positive integral value of $a$, for which all the roots of $x^4-ax^2+9=0$ are real and distinct, is equal to
If $f(x)$ satisfies the relation \[ f(x)=e^x+\int_0^1 (y+x e^x)f(y)\,dy, \] then $e+f(0)$ is equal to
The number of real solutions of the equation: $x|x+3| + |x-1| - 2 = 0$ is
If the equation \[ x^4-ax^2+9=0 \] has four real and distinct roots, then the least possible integral value of $a$ is
Let a function $f(x)$ satisfy \[ 3f(x)+2f\!\left(\frac{m}{19x}\right)=5x \] where $m=\sum_{i=1}^{9} i^2$. Find $f(5)+f(2)$.
If the equation \[ x^4-ax^2+9=0 \] has four real and distinct roots, then the least possible integral value of $a$ is
Let a function $f(x)$ satisfy \[ 3f(x)+2f\!\left(\frac{m}{19x}\right)=5x \] where $m=\sum_{i=1}^{9} i^2$. Find $f(5)+f(2)$.
The number of real roots of the equation $e^{4x} - e^{3x} - 4e^{2x} - e^x + 1 = 0$ is equal to ________.
The number of real roots of the equation $e^{6x} - e^{4x} - 2e^{3x} - 12e^{2x} + e^x + 1 = 0$ is :
Let α, β, γ be the real roots of the equation, x³ + a x² + b x + c = 0, (a, b, c ∈ R and a, b ≠ 0). If the system of equations (in u, v, w) given by α u + β v + γ w = 0; β u + γ v + α w = 0; γ u + α v + β w = 0 has non-trivial solution, then the value of a²/b is :