JEE Main 2026 — Quadratic Equation Questions with Solutions

The smallest positive integral value of a, for which all the roots of x⁴-a x²+9=0 are real and distinct, is equal to

Let a, b, c \1, 2, 3, 4\. If the probability, that ax² + 2√(2) bx + c > 0 for all x R, is (m)/(n), (m, n) = 1, then m +…

If α, β, where α<β, are the roots of the equation λ x²-(λ+3) x+3=0 such that (1)/(α)-(1)/(β)=(1)/(3), then the sum of a…

Consider the quadratic equation (n² - 2n + 2)x² - 3x + (n² - 2n + 2)² = 0, n R. Let α be the minimum value of the produ…

A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete t…

The sum of all the roots of the equation (x-1)²-5|x-1|+6=0, is :

If the quadratic equation (λ+2)x²-3λ x+4λ=0, λ ≠ -2, has two positive roots, then the number of possible integral value…

Let α, β be the roots of the equation x² - 3x + r = 0, and (α)/(2), 2β be the roots of the equation x² + 3x + r = 0. If…

Let α and β be the roots of the equation x²+2 a x+(3 a+10)=0 such that α<1<β. Then the set of all possible values of a…

Let one root of the quadratic equation in x: (k² - 15k + 27)x² + 9(k-1)x + 18 = 0 be twice the other. Then the length o…