Test: Complex Numbers - JEE MCQ

Find the value of 

If the roots of the equation x² - 5x + 16 = 0 are a, b and the roots of the equation x² + px + q = 0 are (a² + b²) and , then-

The number of the integer solutions of x² + 9 < (x + 3)² < 8x + 25 is

The equatiobn π^x = –2x² + 6x – 9 has

Let a > 0, b > 0 and c > 0. Then both the roots of the equation ax² + bx + c = 0

The set of all solutions of the inequality  < 1/4 contains the set

Consider y =, where x is real, then the range of expression y² + y – 2 is

The values of k, for which the equation x² + 2(k – 1) x + k + 5 = 0 possess atleast one positive root, are

If  <= 4, then least and the highest values of 4x² are

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

If the roots of the equation x² + 2ax + b = 0 are real and distinct and they differ by at most 2m, then b lies in the interval

If the roots of the quadratic equation x² + px + q = 0 are tan 30º and tan 15º respectively, then the value of 2 + q – p is

If (1 – p) is root of quadratic equation x² + px + (1 – p) = 0, then its roots are

The values of x and y besides y can satisfy the equation (x, y ∈ real numbers) x²– xy + y² – 4x – 4y + 16 = 0

For what value of a and b the equation x⁴ – 4x³ + ax² + bx + 1 = 0 has four real positive roots ?

If a, b are roots of the equation ax² + bx + c = 0, then the value of a³ + b³ is

If z₁ = 2 + i, z₂ = 1 + 3i, then Re ( z₁ - z₂) =

If a, b are roots of the equation ax² + bx + c = 0 then the equation whose roots are 2a + 3b and 3a + 2b is

If S is the set of all real x such that  is positive, then S contains