HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

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If |z| = 1, then the value of  `(1 + "z")/(1 + "z")` is

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If |z₁| = 1,|z₂| = 2, |z₃| = 3 and |9z₁z₂ + 4z₁z₃ + z₂z₃| = 12, then the value of |z₁ + z₂ + z₃| is

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If z = x + iy is a complex number such that |z + 2| = |z – 2|, then the locus of z is

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The principal argument of the complex number `((1 + "i" sqrt(3))^2)/(4"i"(1 - "i" sqrt(3))` is

Solve the cubic equation: 2x³ – x² – 18x + 9 = 0 if sum of two of its roots vanishes

Solve the equation 9x³ – 36x² + 44x – 16 = 0 if the roots form an arithmetic progression

Solve the equation 3x³ – 26x² + 52x – 24 = 0 if its roots form a geometric progression

Determine k and solve the equation 2x³ – 6x² + 3x + k = 0 if one of its roots is twice the sum of the other two roots

Find all zeros of the polynomial x⁶ – 3x⁵ – 5x⁴ + 22x³ – 39x² – 39x + 135, if it is known that 1 + 2i and `sqrt(3)` are two of its zeros

Solve the cubic equations:

2x³ – 9x² + 10x = 3

Solve the cubic equations:

8x³ – 2x² – 7x + 3 = 0

Solve the equation:

x⁴ – 14x² + 45 = 0

Solve: (x – 5)(x – 7) (x + 6)(x + 4) = 504

Solve: (x – 4)(x – 2)(x- 7)(x + 1) = 16

Solve: (2x – 1)(x + 3)(x – 2)(2x + 3) + 20 = 0

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A zero of x³ + 64 is

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If α, β and γ are the zeros of x³ + px² + qx + r, then `sum 1/alpha` is

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The polynomial x³ – kx² + 9x has three real roots if and only if, k satisfies

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If x³ + 12x² + 10ax + 1999 definitely has a positive zero, if and only if 

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The polynomial x³ + 2x + 3 has