16 solved questions on Complex Numbers and Quadratic Equations, ranging from easy to JEE-Advanced-flavour hard. Click any to see the full solution.
If one root of a quadratic equation is complex, the other root must be its conjugate.
View solution →The condition that the roots of ax²+bx+c=0 are reciprocals of each other is $ac = b$ (True/1/False/0).
View solution →If the roots of x² - px + 6 = 0 are in the ratio 2:3, then p =
View solution →If α and β are roots of ax²+bx+c=0, then α + β =
View solution →If discriminant D > 0, the roots of ax²+bx+c=0 are real and unequal.
View solution →If one root of x² - 5x + k = 0 is twice the other, then k = $x$.
View solution →If α and β are roots of x² - 7x + 12 = 0, then α + β + αβ =
View solution →The discriminant of 2x² - 4x + 3 = 0 is:
View solution →If |z₁ z₂| = |z₁| |z₂| for all complex numbers z₁, z₂.
View solution →If z = re^(iθ), then |z| = $x$.
View solution →The polar form of z = -1 + i is:
View solution →If |z - 1| = 3, then z lies on:
View solution →The argument of a purely imaginary positive number is π/2.
View solution →If z = 4 + 3i, then |z|² = $x$.
View solution →If z = 1 + i, then z⁻¹ =
View solution →The modulus of 3 - 4i is:
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