JEE Advanced Level Test: Complex Numbers- 3 - JEE MCQ

If a, b, c are integers and b² = 4(ac + 5d²), d ∈ N, then roots of the equation ax² + bx + c = 0 are

The set of rational numbers is denoted by

If the inequality (m – 2)x² + 8x + m + 4 > 0 is satisfied for all x Î R, then least integral m is

Find the roots of the equation: x²+ 6x + 5 = 0

If a, b be the roots of 4x² –16x + l = 0, where l ∈ R such that 1 < a < 2 and 2 < b < 3, then the number of integral solutions of l is

If two roots of the equation x³ – px² + qx – r = 0 are equal in magnitude but opposite in sign, then

Find the roots of the equation: 3x² – 3 = 8x

If the quadratic equations 3x² + ax + 1 = 0 and 2x² + bx +1 = 0 have a common root, then the value of the expression 5ab – 2a² – 3b² is

The least value of expression x² + 2xy + 2y² + 4y + 7 is

If a, b, g, d are the roots of the equation x⁴ – Kx³ + Kx² + Lx + M = 0, where K, L & M are real numbers, then the minimum value of a² + b² + g² + d² is

If the roots of the equation x³ + Px² + Qx – 19 = 0 are each one more than the roots of the equation x³ – Ax² + Bx – C = 0, where A, B, C, P & Q are constants, then the value of A + B + C is equal to

The equations x³ + 5x² + px + q = 0 and x³ + 7x² + px + r = 0 have tworoots in common. If the third root of each equation is represented by x₁ and x₂ respectivley, then the ordered pair (x₁, x₂) is

If coefficients of the equation ax² + bx + c = 0, a ¹ 0 are real and roots of the equation are non–real complex and a + c + b < 0, then

If (l² + l – 2)x² + (l + 2) x < 1 for all x ∈ R, then l belongs to the interval

The set of possible values of l for which x² – (l² – 5l + 5)x + (2l² – 3l – 4) = 0 has roots, whose sum and product are both less than 1, is

If the difference between the roots of the equation x² + ax + 1 = 0 is less than √5, then the set of possible values of a is

All the values of m for which both roots of the equation x² – 2mx + m² – 1 = 0 are greater than –2 but less than 4 lie in the interval

The value of a for which the sum of the squares of the roots of the equation x² – (a – 2)x – a – 1 = 0 assume the least value is

If both the roots of the quadratic equation x² – 2kx + k² + k – 5 = 0 are less than 5, then k lies in the interval

If one root of the equation x² + px + 12 = 0 is 4, while the equation x² + px + q = 0 has equal roots then the value of `q' is

If the sum of the roots of the quadratic equation ax² + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a and c/b are in

The value of `a' for which one root of the quadratic equation (a² – 5a + 3)x² + (3a – 1)x + 2 = 0 is twice as large as the other, is