PrepWiser › Learn › Mathematics › Quadratic Equations & Polynomial InequalitiesQuadratic Equations & Polynomial Inequalities — JEE Main PYQs & Practice Questions Quadratic Equations & Polynomial Inequalities is a Mathematics chapter in the JEE Main syllabus. This page brings together 136 previous-year and practice questions on Quadratic Equations & Polynomial Inequalities, organised into 6 topics: Nature of Roots, Relation Between Roots and Coefficients, Transformation of Equations, Location of Roots, Common Roots and Wavy Curve Method. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Nature of Roots The number of elements in the set x ∈ R : (|x| - 3) |x + 4| = 6 is equal to : The number of distinct real roots of x⁴ - 4x + 1 = 0 is : Let a, b, c be the lengths of three sides of a triangle satistying the condition (a²+b²)… The numbers of pairs (a, b) of real numbers, such that whenever α is a root of the… The number of real solutions of the equation 3( x² + 1/x² ) - 2( x + 1/x ) + 5 = 0, is Consider the equation x²+4 x-n=0, where n ∈[20,100] is a natural number. Then the number… The discriminant of 2x² - 4x + 3 = 0 is: The sum of all integral values of k (k ≠ 0) for which the equation 2/(x - 1) - 1/(x - 2)… The number of the real solutions of the equation: x|x+3|+|x-1|-2=0 is The least positive value of 'a' for which the equation 2x² + (a – 10)x + 33/2 = 2a has… If the set of all solutions of |x²+x-9|=|x|+|x²-9| is [α,β]∪ [γ,∞), then ( α²+β²+γ² ) is… Let a , b, c , d and p be any non zero distinct real numbers such that (a² + b² + c²)p²… If the equation a(b-c) x²+b(c-a) x+c(a-b)=0 has equal roots, where a+c=15 and b=36/5… The integer 'k', for which the inequality x² - 2(3k - 1)x + 8k² - 7 > 0 is valid for… If one root of a quadratic equation is complex, the other root must be its conjugate. If the set of all a ∈ R, for which the equation 2 x²+(a-5) x+15=3 a has no real root, is… For p, q ∈ R, consider the real valued function f(x)=(x-p)²-q, x ∈ R and q>0. Let a₁… Let S={sin ² 2 θ:(sin ⁴ θ+cos ⁴ θ) x²+(sin 2 θ) x+(sin ⁶ θ+cos ⁶ θ)=0 has real roots }… The number of real roots of the equation x |x - 2| + 3|x - 3| + 1 = 0 is : The sum of all real values of x for which (3 x²-9 x+17)/(x²+3 x+10)=(5 x²-7 x+19)/(3… Relation Between Roots and Coefficients Let α, β ∈ N be roots of the equation x²-70 x+λ=0, where λ/2, λ/3 ∉ N. If λ assumes the… Let Pₙ=αⁿ+βⁿ, n ∈ N. If P₁₀=123, P₉=76, P₈=47 and P₁=1, then the quadratic equation… For a natural number n, let α ₙ = 19ⁿ - 12ⁿ. Then, the value of (31α ₉ - α ₁₀)/(57α ₈)… If α and β are the roots of the equation 2x(2x + 1) = 1, then β is equal to : Let α₁,α₂,....,α₇ be the roots of the equation x⁷ + 3x⁵ - 13x³ - 15x = 0 and |α ₁| ≥ |α… Let α, β, γ be the three roots of the equation x³+b x+c=0. If β γ=1=-α, then b³+2 c³-3… Let α, β be two roots of the equation x² + (20) 1/4 x + (5) 1/2 = 0. Then α⁸ + β⁸ is… Let α and β be the roots of x² - 3x + p=0 and γ and δ be the roots of x² - 6x + q = 0… The roots of the quadratic equation 3 x²-p x+q=0 are 10ᵗʰ and 11ᵗʰ terms of an… If α and β are roots of ax²+bx+c=0, then α + β = If the roots of x² - px + 6 = 0 are in the ratio 2:3, then p = Let one root of the quadratic equation in x : (k²-15k+27)x²+9(k-1)x+18=0 be twice the… Let α, β be the distinct roots of the equation x²-(t²-5 t+6) x+1=0, t ∈ ℝ and aₙ=αⁿ+βⁿ… Let a, b ∈ R, a ≠ 0 be such that the equation, ax² – 2bx + 5 = 0 has a repeated root α… If the sum of the squares of the reciprocals of the roots α and β of the equation 3x² +… Let α, β be the roots of the equation x²+2 √2 x-1=0. The quadratic equation, whose roots… Let α and β be the roots of x² - 6x - 2 = 0. If aₙ = αⁿ - βⁿ for n ≥ 1, then the value… If the sum of all the roots of the equation e²ˣ - 11eˣ - 45e⁻ˣ + 81/2 = 0 is log ₑp… The condition that the roots of ax²+bx+c=0 are reciprocals of each other is ac = b… If α, β are roots of the equation x² + 5(√2 )x + 10 = 0, α > β and Pₙ = α ⁿ - β ⁿ for… Transformation of Equations Let S={x ∈ R:(√3+√2)ˣ+(√3-√2)ˣ=10}. Then the number of elements in S is : A building construction work can be completed by two masons A and B together in 22.5… The number of points, where the curve f(x)=e⁸ˣ-e⁶ˣ-3 e⁴ˣ-e²ˣ+1, x ∈ ℝ cuts x-axis, is… Let f(x) be a polynomial of degree 3 such that f(k) = - 2/k for k = 2, 3, 4, 5. Then the… The number of real roots of the equation, e⁴ˣ + e³ˣ – 4e²ˣ + eˣ + 1 = 0 is : Let S be the set of all real roots of the equation, 3ˣ(3ˣ – 1) + 2 = |3ˣ – 1| + |3ˣ –… The sum of all the solutions of the equation (8)²ˣ-16 ·(8)ˣ+48=0 is : The value of 4 + 1/(5 + 1/(4 + 1/(5 + 1/(4 + ......∞)))) is : The number of distinct real roots of the equation x⁵(x³-x²-x+1)+x(3 x³-4 x²-2 x+4)-1=0… Let x₁, x₂, x₃, x₄ be the solution of the equation 4 x⁴+8 x³-17 x²-12 x+9=0 and… If α, β are the roots of the equation x²-(5+3^(√(log ₃ 5))-5^(√(log ₅ 3)))x+3(3^((log ₃… The value of 3 + 1/(4 + 1/(3 + 1/(4 + 1/(3 + ....∞)))) is equal to The sum of the squares of the roots of |x-2|² + |x-2| - 2 = 0 and the squares of the… The sum of the roots of the equation x + 1 - 2log ₂(3 + 2ˣ) + 2log ₄(10 - 2⁻ˣ) = 0, is : The product of all the rational roots of the equation (x²-9 x+11)²-(x-4)(x-5)=3, is… The number of real solutions of the equation e⁴ˣ + 4e³ˣ - 58e²ˣ + 4eˣ + 1 = 0 is… The number of real roots of the equation e⁴ˣ - e³ˣ - 4e²ˣ - eˣ + 1 = 0 is equal to… Let S = { x:x ∈ ℝ and (√3 + √2 )^(x² - 4) + (√3 - √2 )^(x² - 4) = 10 }. Then n(S) is… Let S={x³+ax²+bx+c:a,b,c∈ N and a,b,c≤ 20} be a set of polynomials. Then the number of… The sum of all the real roots of the equation (e²ˣ - 4)(6e²ˣ - 5eˣ + 1) = 0 is Location of Roots Common Roots Let λ ≠ 0 be in R. If α and β are the roots of the equation, x² - x + 2λ = 0 and α and γ… Let f(x) be a quadratic polynomial with leading coefficient 1 such that f(0)=p, p ≠ 0… If the value of real number a>0 for which x²-5 a x+1=0 and x²-a x-5=0 have a common real… Let α, β be the roots of the equation x² - 4λ x + 5 = 0 and α, γ be the roots of the… If for some p, q, r ∈ R, not all have same sign, one of the roots of the equation… Let λ ≠ 0 be in R. If α and β are the roots of the equation x² - x + 2λ = 0, and α and γ… Let λ ≠ 0 be a real number. Let α,β be the roots of the equation 14x² - 31x + 3λ = 0 and… Let a be the sum of all coefficients in the expansion of (1-2 x+2 x²)²⁰²³(3-4 x²+2… Wavy Curve Method More Mathematics chapters Frequently asked questions How many Quadratic Equations & Polynomial Inequalities questions are there for JEE Main? PrepWiser has 136 Quadratic Equations & Polynomial Inequalities questions for JEE Main, grouped into 6 topics such as Nature of Roots, Relation Between Roots and Coefficients and Transformation of Equations.
Are these Quadratic Equations & Polynomial Inequalities questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Quadratic Equations & Polynomial Inequalities questions? Open any Quadratic Equations & Polynomial Inequalities question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.