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

If a, b, c ∈ Q and p +√q (p, q ∈ Q) is an irrational root of ax²+bx+c = 0 then the other root is ___________

(a)

-p+√q

(b)

p-iq

(c)

p-√q

(d)

-p-√q

The quadratic equation whose roots are ∝ and β is ___________

(a)

(x - ∝)(x -β) = 0

(b)

(x - ∝)(x + β) = 0

(c)

∝ + β = \(\frac{b}{a}\)

(d)

∝ β = \(\frac{-c}{a}\)

If f(x) = 0 has n roots, then f'(x) = 0 has __________ roots

(a)

n

(b)

n -1

(c)

n+1

(d)

(n-r)

If x is real and \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then ________

(a)

\(\frac{1}{3}\) ≤ k ≤

(b)

k ≥ 5

(c)

k ≤ 0

(d)

none

Let a > 0, b > 0, c >0. Theh n both the root of the equation ax²+bx+c = 0 are _________

(a)

real and negative

(b)

real and positive

(c)

rational numbers

(d)

none

The equation \(\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 } \) has ____________

(a)

no solution

(b)

one solution

(c)

two solution

(d)

more than one solution

lf the root of the equation x³ + bx²+ cx - 1 = 0 form an lncreasing G.P, then ___________

(a)

one of the roots is 2

(b)

one of the roots is 1

(c)

one of the roots is -1

(d)

one of the roots is -2

For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has ________

(a)

one solution

(b)

two solution

(c)

at least two solution

(d)

no solution

If the equation ax²+ bx+c = 0(a > 0) has two roots ∝ and β such that ∝ <- 2 and β > 2, then __________

(a)

b²-4ac = 0

(b)

b² - 4ac <0

(c)

b² - 4ac >0

(d)

b² - 4ac ≥ 0

If \((2+\sqrt{3})^{x^{2}-2 x+1}+(2-\sqrt{3})^{x^{2}-2 x-1}=\frac{2}{2-\sqrt{3}}\) then x = _________

(a)

0, 2

(b)

0, 1

(c)

0, 3

(d)

0, √3

If ∝, β, ૪ are the roots of the equation x³-3x+11 = 0, then ∝+β+૪ is __________.

(a)

0

(b)

3

(c)

-11

(d)

-3

If ∝, β, ૪ are the roots of 9x³-7x+6 = 0, then ∝ β ૪ is __________

(a)

\(\frac{-7}{9}\)

(b)

\(\frac{7}{9}\)

(c)

0

(d)

\(\frac{-2}{3}\)

If x² - hx - 21 = 0 and x² - 3hx + 35 = 0 (h > 0) have a common root, then h = ___________

(a)

0

(b)

1

(c)

4

(d)

3

If ax² + bx + c = 0, a, b, c \(\in\) R has no real zeros, and if a + b + c < 0, then __________

(a)

c>0

(b)

c<0

(c)

c=0

(d)

c≥0

If p(x) = ax² + bx + c and Q(x) = -ax² + dx + c where ac ≠ 0 then p(x). Q(x) = 0 has at least _______ real roots.

(a)

no

(b)

1

(c)

2

(d)

infinite