Mathematics · 2026
JEE Main · 21 January 2026, Shift 2 · Q4
Let α and β be the roots of the equation x^2+2 a x+(3 a +10)=0 such that α<1<β. Then the set of all possible values of a is:
Let $\displaystyle \alpha$ and $\displaystyle \beta$ be the roots of the equation $\displaystyle x^2+2 \mathrm{a} x+(3 \mathrm{a}+10)=0$ such that $\displaystyle \alpha<1<\beta$. Then the set of all possible values of a is :
Official answer
From NTA’s final answer key for this paper.
(3)
$\displaystyle \left(-\infty, \frac{-11}{5}\right)$
More from Quadratic Equations
- 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 G.P., then |p+q|…2026
- 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 equation x^2+6 x=m…2026
- 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 the roots of the…2026
- 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 minimum. Then the…2026
- 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:2026
- 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 rectum of the parabola…2026
- 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 is equal to:2026
- 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 is:2026
JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.