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

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

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 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

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 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

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

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 ∝, 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 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