MCQ (Previous Year Questions) - Complex Numbers (Competition Level 1) - JEE MCQ

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, 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- 

The number of real solutions of the equation x² – 3 |x| + 2 = 0 is

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

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-

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 the roots of the equation x² – bx + c = 0 be two consecutive integers, then b²– 4c equals- 

In a triangle PQR, ∠R = , If tan  and tan  are the roots of ax² + bx+c = 0, a < 0 then -

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 the roots of the quadratic equation x²+px+q=0 are tan 30º and tan15º, respectively then the value of 2 + q – p 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

If x is real, the maximum value of  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-

The quadratic equations x² – 6x + a = 0 and x² – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is 

How many real solution does the equation x⁷ + 14x⁵ + 16x³ + 30x - 560 = 0 have ?

If the roots of the equation bx² + cx + a = 0 be imaginary, then for all real values of x, the expression 3b²x² + 6bcx + 2c² is -  

If a and b are the roots of the equation x² – x + 1 = 0, then a²⁰⁰⁹ + b²⁰⁰⁹ = 

The equation e^{sin x} – e^{_sin x} – 4 = 0 has :