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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 : 15
10 x 1 = 10
1. If α,β and γ are the roots of x3+px2+qx+r, then $\Sigma \frac { 1 }{ \alpha }$ is

(a)

-$\frac { q }{ r }$

(b)

$\frac { p }{ r }$

(c)

$\frac { q }{ r }$

(d)

-$\frac { q }{ p }$

2. 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

3. 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

4. The number of positive zeros of the polynomial $\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }$(-1)rxr is

(a)

0

(b)

n

(c)

< n

(d)

r

5. 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

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

7. Ifj(x) = 0 has n roots, thenf'(x) = 0 has __________ roots

(a)

n

(b)

n -1

(c)

n+1

(d)

(n-r)

8. 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

9. Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

(a)

real and negative

(b)

real and positive

(c)

rational numb rs

(d)

none

10. 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

11. 5 x 1 = 5
12. 6x6 - 35x5 + 56x4 -56x2 + 35x - 6 = 0

13. (1)

at least 6 imaginary roots

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

15. (2)

4 Change of sign

16. 2x7-3x6-4x5+5x4+6x3-7x+8 = 0

17. (3)

Reciprocal equation of type I

18. 9x9+2x5-x4-7x2+2=0

19. (4)

4 Change of sign

20. x9-5x8 -14x7=0

21. (5)

even degree reciprocal equation of type II