If α, β and γ are the zeros of x³ + px² + qx + r, then \(\Sigma \frac { 1 }{ \alpha } \) is

(a)

\(-\frac { q }{ r } \)

(b)

\(-\frac { p }{ r } \)

(c)

\(\frac { q }{ r } \)

(d)

\(-\frac { q }{ p } \)

According to the rational root theorem, which number is not possible rational zero of 4x⁷ + 2x⁴ - 10x³ - 5?

(a)

-1

(b)

\(\frac { 5 }{ 4 } \)

(c)

\(\frac { 4 }{ 5 } \)

(d)

5

The number of real numbers in [0, 2π] satisfying sin⁴x - 2sin²x + 1 is

(a)

2

(b)

4

(c)

1

(d)

∞

The polynomial x³ + 2x + 3 has

(a)

one negative and two imaginary zeros

(b)

one positive and two imaginary zeros

(c)

three real zeros

(d)

no zeros

The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)^rx^r is

(a)

0

(b)

n

(c)

< n

(d)

r

If α, β, and γ are the roots of the equation x³ + px² + qx + r = 0, find the value of  \(\Sigma \frac { 1 }{ \beta \gamma } \) in terms of the coefficients.

A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was left standing.

Solve the equations:
6x⁴- 35x³+ 62x²- 35x + 6 = 0

Find the sum of the squares of the roots of ax⁴+ bx³+ cx²+ dx + e = 0. \(a \neq 0\)

If the roots of x³+ px²+ qx + r = 0 are in H.P. prove that 9pqr = 27r²+2q³.

Solve the equation
2x³ - 9x² + 10x = 3

Solve the equation (x-2) (x-7) (x-3) (x+2)+19 = 0

Solve the equation (2x-3) (6x-1) (3x-2) (x-2)-5 = 0