Question

Q.43)
un - 10un - 1 + 9un - 2=0 find out the roots? (1 marks )
Ans.
10,1
7,2
1,9
4,5​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The roots of

$\sf{u_{n} - 10u_{n - 1} + 9u_{n - 2} = 0}$

• 10 , 1

• 7 , 2

• 1 , 9

• 4 , 5

EVALUATION

Here the given equation is

$\sf{u_{n} - 10u_{n - 1} + 9u_{n - 2} = 0}$

So the auxiliary equation is

$\sf{ {x}^{2} - 10x + 9 = 0}$

$\sf{ \implies \: {x}^{2} - (9 + 1)x + 9 = 0}$

$\sf{ \implies \: {x}^{2} - 9x - x+ 9 = 0}$

$\sf{ \implies \: x(x - 9) - 1(x - 9) = 0}$

$\sf{ \implies \: (x - 9) (x - 1) = 0}$

$\sf{ \implies \: x = 9 \: , \: 1}$

Hence the required roots are 1 , 9

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Answer 2

Question ⤵️

Q.43) un - 10un - 1 + 9un - 2=0 find out the roots?

Ans.

○10,1

○7,2

○1,9

○4,5

Answer ⤵️

TO CHOOSE THE CORRECT OPTION

The roots of:-

$\sf{u_{n} - 10u_{n - 1} + 9u_{n - 2} = 0}$

○10 , 1

○7 , 2

○1 , 9

○4 , 5

Calculation ⤵️

given equation is:-

$\sf{u_{n} - 10u_{n - 1} + 9u_{n - 2} = 0}$

Therefore the auxiliary equation is:-

$\sf{ {x}^{2} - 10x + 9 = 0}$

$\sf{ \implies \: {x}^{2} - (9 + 1)x + 9 = 0}$

$\sf{ \implies \: {x}^{2} - 9x - x+ 9 = 0}$

$\sf{ \implies \: x(x - 9) - 1(x - 9) = 0}$

$\sf{ \implies \: (x - 9) (x - 1) = 0}$

$\sf{ \implies \: x = 9 \: , \: 1}$

Therefore the required roots are 1 , 9.

Therefore option 3. 1 , 9 is your correct answer.

un - 10un - 1 + 9un - 2=0 find out the roots?

Ans.

○10,1

○7,2

✔1,9

○4,5

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