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#### Theory of Equations One Mark Questions

12th Standard EM

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Maths

Time : 00:30:00 Hrs
Total Marks : 10
5 x 1 = 5
1. A zero of x3 + 64 is

(a)

0

(b)

4

(c)

4i

(d)

-4

2. If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

(a)

mn

(b)

m+n

(c)

mn

(d)

nm

3. A polynomial equation in x of degree n always has

(a)

n distinct roots

(b)

n real roots

(c)

n imaginary roots

(d)

at most one root

4. 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

5. 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=$\frac{-c}{a}$

6. 5 x 1 = 5
7. 6x6 - 35x5 + 56x4 -56x2 + 35x - 6 = 0

8. (1)

at least 6 imaginary roots

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

10. (2)

4 Change of sign

11. 2x7-3x6-4x5+5x4+6x3-7x+8 = 0

12. (3)

even degree reciprocal equation of type II

13. 9x9+2x5-x4-7x2+2=0

14. (4)

4 Change of sign

15. x9-5x8 -14x7=0

16. (5)

Reciprocal equation of type I