List of top Mathematics Questions on Complex Numbers and Quadratic Equations asked in JEE Advanced

In the quadratic equation $p(x) = 0$ with real coefficients has purely imaginary roots. Then, the equation $p[p(x)] = 0 $ has

Let $w = \frac{\sqrt 3 + i }{2}$ and $P = \{W^n:n=1,2,3,....\}$ Further $H_1 = \bigg \{z \in C: Re \, z >\frac{1}{2}\bigg \}$ and $H_2=\bigg[ z\in C: Re \,z

A value of $b$ for which the equations $x^2+bx-1=0,x^2+x+b=0$ have one root in common is

Let $z = \cos \theta + i \sin \theta$. Then, the value of $\displaystyle \sum _{m=0}^{15} Im (z^{2m-1})$ at $\theta = 2^\circ$ is

Let $\alpha$, $\beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2},2\beta$ be the roots of the equation $x^2-qx+r=0.$ Then, the value of r is

A man walks a distance of 3 units from the origin towards the North-East (N 45$^{\circ}$ E) direction. From there, he walks a distance of 4 units towards the North-West (N 45$^\circ$ W) direction to reach a point P. Then, the position of P in the Arg and plane is

If a, b,c are the sides of a triangle ABC such that $x^2 - 2(a+b+c)x+3\lambda(ab+bc+ca)=0$ has real roots, then

The shaded region, where $P = (-1,0), Q = (-1 + \sqrt 2,\sqrt 2 )R = (-1 + \sqrt 2,-\sqrt 2), S = (1,0)$ is represented by

The minimum value of $| a + b\omega + c \omega^2|$ , where $ a, b$ and $c$ are all not equal integers and $\omega \, (\ne 1)$ is a cube root of unity, is

If one root is square of the other root of the equation $x^2+px+q=0,$ then the relation between p and q is

If $\omega (\ne 1)$ be a cube root of unity and $(1 + \omega^2)^n = (1 + \omega^4)^n,$ then the least positive value of n is

The complex numbers $z_1, z_2$ and $z_3$ satisfying $\frac{z_1-z_3}{z_2-z_3}=\frac{1-i \sqrt 3}{2}$ are the vertices of a triangle which is

Let $z_1$ and $z_2$ be nth roots of unity which subtend a right angled at the origin, then n must be of the form (where, k is an integer)

If $\alpha$ and $\beta$ are $(\alpha < \beta)$ the roots of the equation $x^2+bx+c=0,$ where $c < 0 < b$,the

For the equation $3x^2+px+3=0,p>0,$ if one of the root is square of the other, then p is equal to

If $ i = \sqrt -1$ then $ 4 + 5 \bigg(-\frac{1}{2}+\frac{i\sqrt 3}{2}\bigg)^{334}+3\bigg(-\frac{1}{2}+\frac{i\sqrt 3}{2}\bigg)^{365}$ is equal to

The value of $\displaystyle \sum_{k=1}^6 \bigg(\sin\frac{2\pi k}{7}-i \cos \frac{2\pi k}{7}\bigg)$ is

If $\omega$ is an imaginary cube root of unity, then (1 + $\omega$ - $\omega^2)^7$ is equal to

The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ has

Let $ \alpha, \beta $ be the roots of the equation,$(x - a) (x - b) = c, c \ne 0 $.Then the roots of the equation $ (x - \alpha) \, (x - \beta) + c = 0 $ are

Both the roots of the equation $(x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0$ are always