Quadratic Equations in Complex Numbers: JEE Questions & Solutions

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

The number of distinct real solutions of the equation x|x + 4| + 3|x + 2| + 10 = 0 is

Let α, β be the roots of the quadratic equation 12x² - 20x + 3λ = 0, λ ∈ ℤ. If 1/2 ≤ |β-α| ≤ 3/2, then the sum of all possible values of λ…

If α and β (α < β) are the roots of the equation (-2 + √3)|√x - 3| + (x - 6√x) + (9 - 2√3) = 0, x ≥ 0, then √(β/α) + √αβ is equal to:

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

The number of real solutions of the equation: x|x+3| + |x-1| - 2 = 0 is

Let S = {x³ + ax² + bx + c: a, b, c ∈ ℕ and a, b, c ≤ 20} be a set of polynomials. Then the number of polynomials in S, which are divisible…

The product of all solutions of the equation e^(5(logₑ x)² + 3) = x⁸, x > 0, is:

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

If α + iβ and γ + iδ are the roots of the equation x² - (3-2i)x - (2i-2) = 0, i = √(-1), then αγ + βδ is equal to:

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

Let S = {x ∈ ℝ: (√3 + √2)^x + (√3 - √2)^x = 10}. Then the number of elements in S is:

The sum of all solutions of the equation 8^2x - 16 · 8^x + 48 = 0 is:

If the value of real number a > 0 for which x² - 5ax + 1 = 0 and x² - ax - 5 = 0 have a common real root is 3/√2β, then β is equal to

Let α, β be the roots of the quadratic equation x² + √6x + 3 = 0. Then, (α²³ + β²³ + α¹⁴ + β¹⁴)/(α¹⁵ + β¹⁵ + α¹⁰ + β¹⁰) is equal to: