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 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 = \(\frac{-c}{a}\)

6x⁶ - 35x⁵ + 56x⁴ -56x² + 35x - 6 = 0

(1)

even degree reciprocal equation of type II

p(x) = xⁿ.p\(\left( \frac { 1 }{ x } \right) \)

(2)

Reciprocal equation of type I

2x⁷-3x⁶-4x⁵+5x⁴+6x³-7x+8 = 0

(3)

4 Change of sign

9x⁹+2x⁵-x⁴-7x²+2 = 0

(4)

at least 6 imaginary roots

x⁹-5x⁸ -14x⁷= 0

(5)

4 Change of sign