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

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 ∝, 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 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 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