Nature of Roots

JEE Main Mathematics · Quadratic Equations · 6 questions, latest first

• Consider the equation x^2+4 x-n=0, where n ∈[20,100] is a natural number. Then the number of all distinct values of n, for which…20254 April, Shift 1 · Q3
• Let the equation x(x+2)(12-k)=2 have equal roots. Then the distance of the point (k, k/2) from the line 3 x+4 y+5=0 is20253 April, Shift 2 · Q4
• If the set of all a ∈ R, for which the equation 2 x^2+(a-5) x+15=3 a has no real root, is the interval (α, β), and X={x ∈ Z:…202529 January, Shift 2 · Q3
• If the equation a(b-c) x^2+b(c-a) x+c(a-b)=0 has equal roots, where a+c=15 and b=36/5, then a^2+c^2 is equal to ____202523 January, Shift 1 · Q21
• Let S={ sin^2 2 θ:( sin^4 θ+ cos^4 θ) x^2+( sin 2 θ) x+( sin^6 θ+ cos^6 θ)=0. has real roots }. If α and β be the smallest and…20244 April, Shift 2 · Q22
• Let a, b, c be the lengths of three sides of a triangle satistying the condition (a^2+b^2) x^2-2 b(a+c) x+(b^2+c^2)=0. If the set…202431 January, Shift 2 · Q24