Quadratic Equations & Polynomial Inequalities JEE Main PYQs PDF, 2020–2026

Quadratic Equations & Polynomial Inequalities questions per year

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 128 of the 129 asked.

Topic-wise weightage by year

How many Quadratic Equations & Polynomial Inequalities questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 21 JEE Main 2026 Quadratic Equations & Polynomial Inequalities questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Nature of Roots

   The sum of squares of all the real solutions of the equation $\log_{(x+1)}\left(2x^{2}+5x+3\right)=4-\log_{(2x+3)}\left(x^{2}+2x+1\right)$ is equal to $\_\_\_\_$.

   Solve it online →

2. JEE Main 2026 · 6 Apr · Shift 2 · Location of Roots

   Let $\underset{{x\rightarrow 2}}{lim}\frac{(\tan (x-2))\left({\mathrm{r}}x^{2}+({\mathrm{p}}-2)x-2{\mathrm{p}}\right)}{(x-2)^{2}}=5$ for some ${\mathrm{r}},{\mathrm{p}}\in \boldsymbol{R}$. If the set of all possible values of q , such that the roots of the equation ${\mathrm{r}}x^{2}-{\mathrm{p}}x+{\mathrm{q}}=0$ lie in $(0,2)$, be the interval $(\alpha,\beta]$, then $4(\alpha+\beta)$ equals :

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3. JEE Main 2026 · 6 Apr · Shift 1 · Relation Between Roots and Coefficients

   Let one root of the quadratic equation in $x$ :

   $\left(k^{2}-15k+27\right)x^{2}+9(k-1)x+18=0$

   be twice the other. Then the length of the latus rectum of the parabola $y^{2}=6kx$ is equal to:

   Solve it online →

4. JEE Main 2026 · 6 Apr · Shift 1 · Location of Roots

   Let $e_{1}$ and $e_{2}$ be two distinct roots of the equation $x^{2}-ax+2=0$. Let the sets $\{a\in {\mathbb{R}}:e_{1}$ and $e_{2}$ are the eccentricities of hyperbolas $\}=(\alpha,\beta)$, and $\{a\in {\mathbb{R}}:e_{1}$ and $e_{2}$ are the eccentricities of an ellipse and a hyperbola, respectively $\}=(\gamma,\infty)$.

   Then $\alpha^{2}+\beta^{2}+\gamma^{2}$ is equal to:

   Solve it online →

5. JEE Main 2026 · 5 Apr · Shift 2 · Relation Between Roots and Coefficients

   Let $\alpha,\beta$ be the roots of the equation $x^{2}-x+{\mathrm{p}}=0$ and $\gamma,\delta$ be the roots the equation $x^{2}-4x+{\mathrm{q}}=0$; $p,q\in {\mathbf{Z}}$. If $\alpha,\beta,\gamma,\delta$ are in G.P., then $|p+q|$ equals :

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6. JEE Main 2026 · 4 Apr · Shift 1 · Nature of Roots

   If the set of all solutions of $\left|x^{2}+x-9\right|=|x|+\left|x^{2}-9\right|$ is $[\alpha,\beta]\cup [\gamma,\infty)$, then ( $\alpha^{2}+\beta^{2}+\gamma^{2}$ ) is equal to:

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7. JEE Main 2026 · 4 Apr · Shift 2 · Location of Roots

   If the quadratic equation $(\lambda+2)x^{2}-3\lambda x+4\lambda=0,\lambda\neq -2$, has two positive roots, then the number of possible integral values of $\lambda$ is :

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8. JEE Main 2026 · 2 Apr · Shift 1 · Relation Between Roots and Coefficients

   Let $\alpha,\alpha+2,\alpha\in {\mathbf{Z}}$, be the roots of the quadratic equation $x(x+2)+(x+1)(x+3)+(x+2)(x+4)+\ldots.+(x+{\mathrm{n}}-1)(x+{\mathrm{n}}+1)=4{\mathrm{n}}$ for some ${\mathrm{n}}\in {\mathbf{N}}$. Then ${\mathrm{n}}+\alpha$ is equal to :
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9. JEE Main 2026 · 2 Apr · Shift 2 · Relation Between Roots and Coefficients

   Let $\alpha,\beta$ be the roots of the equation $x^{2}-3x+r=0$, and $\frac{\alpha}{2},2\beta$ be the roots of the equation $x^{2}+3x+r=0$.

   If the roots of the equation $x^{2}+6x=m$ are $2\alpha+\beta+2r$ and $\alpha-2\beta-\frac{r}{2}$, then $m$ is equal to :

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10. JEE Main 2026 · 28 Jan · Shift 1 · Relation Between Roots and Coefficients

    If $\alpha,\beta$, where $\alpha<\beta$, are the roots of the equation $\lambda x^{2}-(\lambda+3)x+3=0$ such that $\frac{1}{\alpha}-\frac{1}{\beta}=\frac{1}{3}$, then the sum of all possible values of $\lambda$ is

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11. JEE Main 2026 · 28 Jan · Shift 1 · Transformation of Equations

    Let ${\mathrm{S}}=\left\{x^{3}+ax^{2}+bx+c:a,b,c\in {\ \mathrm{N}}\right.$ and $a,b,c\leq 20\}$ be a set of polynomials. Then the number of polynomials in S , which are divisible by $x^{2}+2$, is

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12. JEE Main 2026 · 24 Jan · Shift 2 · Nature of Roots

    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

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Sample questions from recent papers

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