Quadratic Equations

JEE Main Mathematics · 11 questions

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• Consider the quadratic equation (n^2-2 n+2) x^2-3 x+(n^2-2 n+2)^2=0, n ∈ R. Let α be the minimum value of the product of its…20266 April, Shift 2 · Q2
• Let lim_x → 2 (( tan (x-2))(r x^2+(p-2) x-2 p))/((x-2)^2)=5 for some r, p ∈ R. If the set of all possible values of q, such that…20266 April, Shift 2 · Q16
• Let one root of the quadratic equation in x: (k^2-15 k+27) x^2+9(k-1) x+18=0 be twice the other. Then the length of the latus…20266 April, Shift 1 · Q2
• Let e_1 and e_2 be two distinct roots of the equation x^2-a x+2=0. Let the sets {a ∈ R: e_1. and e_2 are the eccentricities of…20266 April, Shift 1 · Q3
• Let α, β be the roots of the equation x^2-x+p=0 and γ, δ be the roots the equation x^2-4 x+q=0; p, q ∈ Z. If α, β, γ, δ are in…20265 April, Shift 2 · Q1
• Let a, b ∈ C. Let α, β be the roots of the equation x^2+a x+b=0. If β-α=√11 and β^2-α^2=3 i √11, then (β^3-α^3)^2 is equal to:20265 April, Shift 1 · Q1
• If α=1 and β=1+i √2, where i=√-1 are two roots of the equation x^3+a x^2+b x+c=0, a, b, c ∈ R, then ∫_-1^1(x^3+a x^2+b x+c) d x…20264 April, Shift 2 · Q4
• If the quadratic equation (λ+2) x^2-3 λ x+4 λ=0, λ ≠-2, has two positive roots, then the number of possible integral values of λ…20264 April, Shift 2 · Q5
• Let α, β be the roots of the equation x^2-3 x+r=0, and (α)/2, 2 β be the roots of the equation x^2+3 x+r=0. If the roots of the…20262 April, Shift 2 · Q1
• Let the parabola y=x^2+p x+q passing through the point ( 1,-1 ) be such that the distance between its vertex and the x -axis is…20262 April, Shift 2 · Q12
• Let α, α+2, α ∈ Z, be the roots of the quadratic equation x(x+2)+(x+1)(x+3)+(x+2)(x+4)+….+(x+n-1)(x+n+1)=4 n for some n ∈ N. Then…20262 April, Shift 1 · Q1