Choose the correct alternative:The number of positive roots of the polynomials njnCrrr∑j=0n nCr(-1)rxr is

Choose the correct alternative:
The number of positive roots of the polynomials `sum_("j" = 0)^"n" ""^"n""C"_"r" (- 1)^"r" x^"r"` is

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Chapter 3: Theory of Equations - Exercise 3.7 [Page 128]

Chapter 3 Theory of Equations
Exercise 3.7 | Q 10 | Page 128

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

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

Solve the cubic equations:

2x³ – 9x² + 10x = 3

Solve the equation:

x⁴ – 14x² + 45 = 0

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

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

Choose the correct alternative:
A zero of x³ + 64 is

Choose the correct alternative:
The polynomial x³ – kx² + 9x has three real roots if and only if, k satisfies

Choose the correct alternative:
If x³ + 12x² + 10ax + 1999 definitely has a positive zero, if and only if

Choose the correct alternative:
The polynomial x³ + 2x + 3 has