Location of Roots

JEE Main Mathematics · Quadratic Equations · 7 questions, latest first

• 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 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
• 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 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:202621 January, Shift 2 · Q4
• Let the set of all values of p ∈ R, for which both the roots of the equation x^2-(p+2) x+(2 p+9)=0 are negative real numbers, be…20257 April, Shift 1 · Q3
• If the set of all a ∈ R-{1}, for which the roots of the equation (1-a) x^2+2(a-3) x+9=0 are positive is (-∞,-α] ∪[β, γ), then 2…20252 April, Shift 2 · Q21
• The number of integral values of k, for which one root of the equation 2 x^2-8 x+k=0 lies in the interval (1,2) and its other…20231 February, Shift 2 · Q63