Complex Numbers and Quadratic Equation - 2 - Free MCQ Test with solutions

Each pair of equations from x² – b_rx + c_r = 0, r = 1, 2, 3 have a common root and the relation is given ∑b₁² + 4 ∑c₁ = k∑b₁b₂ then value of k is -

If the product of the roots of the equation αx² + bx + α² + 1 = 0 is –2, then  equals -

|2x – 3| < |x + 5|, then x belongs to

If tan A and tan B are the roots of the quadratic x² – qx + p = 0 then the value of cos² (A + B) is -

The values of ‘a’ for which exactly one root of the equation e^ax² – e^2a x + e^a – 1 = 0 lies between 1 and 2 are given by -

If roots of equation x² – 2ax + (a² + a – 3) = 0 are real and less than 3 then

The value of the expression x⁴ – 8x³ + 18x² – 8x + 2 when x = 2 + √3 is

The values of 'a' for which (a² – 1)x² + 2 (a – 1) x + 2 is positive for any x is -

The set of real roots of the equation log_{(5x + 4)} (2x + 3)³ – log_{(2x + 3)} (10x² + 23x + 12) = 1 is -

If x + y + z = 5 and xy + yz + zx = 3, then least and largest value of x are

The expression y = ax² + bx + c has always the same sign as c if -

If p, q, r, s are rational numbers & roots of f(x) = 0 are eccentricities of a parabola & a rectangular hyperbola where f(x) = px³ + qx² + rx + s, then p + q + r + s =

If r and s are positive, then roots of the equation x² – rx – s =0 are -

Let α,β be the roots of x² + (3 – λ)x – λ = 0. The value of λ for which α² + β² is minimum, is -

Number of values of z (real or complex) simultaneously satisfying the system of equations 1 + z + z² + z³ + .......... + z¹⁷ = 0 and 1 + z + z² + z³ + .......... + z¹³ = 0 is

The complex number z having least positive argument which satisfy the condition |z – 25i | ≤ 15 is -

Let Z₁ = (8 + i)sin θ + (7 + 4i)cos θ and Z₂ = (1 + 8i)sin θ + (4 + 7i)cos θ are two complex numbers. If Z₁ · Z₂ = a + ib where a, b ∈ R then the largest value of (a + b) ∀ θ ∈ R, is

A point 'z' moves on the curve |z – 4 – 3 i| = 2 in an argand plane. The maximum and minimum values of |z| are