#### Theory of Equations Book Back Questions

12th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
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. According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

(a)

-1

(b)

$\frac { 5 }{ 4 }$

(c)

$\frac { 4 }{ 5 }$

(d)

5

3. The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 is

(a)

2

(b)

4

(c)

1

(d)

4. The polynomial x3+2x+3 has

(a)

one negative and two real roots

(b)

one positive and two imaginary roots

(c)

three real roots

(d)

no solution

5. 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

6. 3 x 2 = 6
7. If α, β, and γ are the roots of the equatio x3+pz2+qx+r=0, find the value of  $\Sigma \frac { 1 }{ \beta \gamma }$ in terms of the coefficients.

8. A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was cut away.

9. Solve the equations:
6x4-35x3+62x2-35x+6=0

10. 3 x 3 = 9
11. Find the sum of the squares of the roots of ax4+bx3+cx2+dx+e = 0.

12. If the roots of x3+px2+qx+r=0 are in H.P. prove that 9pqr = 27r3+2p.

13. Solve the cubic equations:
8x3-2x2-10x+3=0

14. 2 x 5 = 10
15. Solve the equation (x-2)(x-7)(x-3)(x+2)+19=0

16. Solve the equation (2x-)(6x-1)(3x-2)(x-12)-7=0