A zero of x³ + 64 is

(a)

0

(b)

4

(c)

4i

(d)

-4

If f and g are polynomials of degrees m and n respectively, and if h(x) = (f ^_o g)(x), then the degree of h is

(a)

mn

(b)

m+n

(c)

mⁿ

(d)

n^m

A polynomial equation in x of degree n always has

(a)

n distinct roots

(b)

n real roots

(c)

n complex roots

(d)

at most one root

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 polynomial x³ - kx² + 9x has three real zeros if and only if, k satisfies

(a)

|k| ≤ 6

(b)

k = 0

(c)

|k| > 6

(d)

|k| ≥ 6

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

(a)

2

(b)

4

(c)

1

(d)

∞

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

(a)

a ≥ 0

(b)

a > 0

(c)

a < 0

(d)

a ≤ 0

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