Question

Question 1
Write an irrational number between 2 and 2.2

Question 2
If x2 = 64 and x > 0, find the value of x13+x0

Question 3
If x=2–√−1, then write the value of x+1x

Question 4
Write a trinomial of degree 4

Question 5
Find three rational numbers between 25and37.

Question 6
If x=5√+3√5√−3√ and y=5√−3√5√+3√ then find x+y+xy.

Question 7
Show that (xa+b)2(xb+c)2(xc+a)2(xaxbxc)4=1

Question 8
If x = - 3 is a zero of the polynomial p(x) = 4x3 – 10x2 + kx – 6. Find the value of k.

Question 9
If f(x) = x4 – 2x3 + 3x2 – ax + b is a polynomial such that when it is divided by x – 1 and x + 1, the remainders are respectively 5 and 19. Find the values of a and b. Also, write the final polynomial f(n).

Question 10
Find the value of x, 5x - 3 . 32x - 8 = 225.

Question 11
If both a and b are rational numbers, find the values of a and 2√+3√32√−23√=a−b6–√​

Answer 1

Given : number   2 and 2.2

To find : an irrational number between 2 and 2.2

Solution:

an irrational number between 2 and 2.2

2² = 4

2.2² = 4.84

√4.5   is an irrational number between  2 and 2.2

√4.5  = 3/√2

3/√2  is an irrational number between  2 and 2.2

x² = 64

=> x = 8   as  x > 0

If x = - 3 is a zero of the polynomial p(x) = 4x³– 10x² + kx – 6. Find the value of k.

p(-3) = 0

=> 4(-3)³ - 10(-3)² + k(-3)  - 6 = 0

=> -108 - 90 -3k - 6 = 0

=> 3k = -204

=> k = - 68

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