JEE Main 2025 — Quadratic Equation Questions with Solutions

Let Pn=αⁿ+βⁿ, n N. If P₁₀=123, P₉=76, P₈=47 and P₁=1, then the quadratic equation having roots (1)/(α) and (1)/(β) is :

The number of solutions of the equation ((9)/(x)-9√(x)+2 ) ((2)/(x)-7√(x)+3 )=0 is:

The sum, of the squares of all the roots of the equation x²+|2 x-3|-4=0, is

If the set of all a R, for which the equation 2 x²+(a-5) x+15=3 a has no real root, is the interval (α, β), and X=\x Z:…

Let αθ and βθ be the distinct roots of 2 x²+( θ) x-1=0, θ (0,2 π). If m and M are the minimum and the maximum values of…

Let the set of all values of p R, for which both the roots of the equation x²-(p+2) x+(2 p+9)=0 are negative real numbe…

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), then a²+c² is equal to

For t -1, let and be the roots of the equation ((t+2)⁽¹⁾/⁽⁷⁾-1 ) x²+ ((t+2)⁽¹⁾/⁽⁶⁾-1 ) x+ ((t+2)⁽¹⁾/⁽²¹⁾-1 )=0 If t →₋₁…

If the set of all a R-\1\, for which the roots of the equation (1-a) x²+2(a-3) x+9=0 are positive is (-∞,-α] [β, γ), th…

Consider the equation x²+4 x-n=0, where n [20,100] is a natural number. Then the number of all distinct values of n, fo…