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

Let $p, q, r \,\in\, R$ and $r > p > 0$. If the quadratic equation $px^2 + qx + r = 0$ has two complex roots $\alpha$ and $\beta$, then $\left|\alpha\right|+\left|\beta\right|$ is

Let for $a \ne a_{1} \ne 0$, $f\left(x\right) = ax^{2} + bx + c, g^{9}x) = a_{1}x^{2} + b_{1}x + c_{1}$ and $p\left(x\right) = f\left(x\right) - g\left(x\right)$. If $p\left(x\right) = 0$ only for $x = -1$ and $p\left(-2\right) = 2$, then the value of $p\left(2\right)$ is :

Let $z_1$ and $z_2$ be two distinct complex numbers and let $z = (1 - t) z_1 + tz_2$ for some real number t with $0 < t < 1$. If $arg (w) $ denotes the principal argument of a non-zero complex num ber w, then

If $\alpha$ and $\beta$ are the roots of the equation $x^{2} - x + 1 = 0$, then $\alpha^{2009} + \beta^{2009} =$

If $\left|Z-\frac{4}{z}\right|=2$, then the maximum value of $\left|Z\right|$ is equal to

All the values of m for which both roots of the equation $x^{2}-2mx+m^{2}-1=0$ are greater than -2but less than 4 lie in the interval :

If x is real, the maximum value of $\frac{3x^2 + 9x + 17}{3x^2 + 9x + 7}$ is

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

If $(1 - p)$ is a root of quadratic equation $x^2 + px + (1- p) = 0$, then its roots are

If $\left(\frac{1+i}{1-i}\right)^{x}=1,$ then

If $z$ and $?$ are two non-zero complex numbers such that $|z?| = 1$, and Arg $(z)$ - Arg $\left(\omega\right)=\frac{\pi}{2},$ then $\bar{z}\omega$ is equal to

Let z and w be two complex numbers such that $|z| \le 1, |w | \le 1$ and $|z + i w |= | z - \overline {iw}| = 2$ , then z equals

If $z_1$ and $z_2$ are two non-zero complex numbers such that $| z_1+ z_2| = | z_1| + | z_2|$ , then $arg (z_1 ) - arg (z_2)$ is equal to