Question

• 9. Write a pair of irrational numbers whose
difference is irrational.
10. Write a pair of irrational numbers whos
difference is rational.
11. Write a pair of irrational numbers whos
product is irrational.
• 12. Write a pair of irrational numbers who
product is rational.
13. Write in ascending order :
(1) 315 and 4,3
(ii) 235 and 332
(iii) 65,713 and 8/2
14) Write in descending order :
(1) 26 and 342 (ii) 73 and 317
15. Compare :
(1) 15 and V12
(ii) 24 and 2
16. Insert two irrational numbers betw
5 and 6.
17. Insert five irrational numbers between 2
and 3 13.​

Answer 1

Answer:

Let ax + b be subtracted from p(x)=x  

3

−6x  

2

−15x+80

so that it is exactly divisible by x  

2

+x−12.

∴s(x)=x  

3

−6x  

2

−15x+80−(ax+b)

=x  

3

−6x  

2

−(15+a)x+(80−b)

Dividend = Divisor × quotient + remainder

But remainder will be zero.

∴ Dividend = Divisor × quotient

⇒s(x)=(x  

2

+x−12)×quotient

⇒s(x)=x  

3

−6x  

2

−(15+a)x+(80−b)

Hence, x(4−a)+(−4−b)=0,x



=0

⇒4−a=0 & (−4−b)=0

⇒a=4 and b=−4

Hence, if in p(x) we subtract 4x - 4 then it is exactly divisible by x  

2

+x−12