Algebra Ex 3.8-10th Std Maths-Book Back Question And Answer
Question 1.
Find the square root of the following polynomials by division method
(i) x4 – 12x3 + 42x2 – 36x + 9
Answer::
(ii) 31 x2 – 28x3 + 4x4 + 42x + 9
Answer:
Rearrange the order we get
4x4 – 28x3 + 37x2 + 42x + 9
(iii) 16x4 + 8x2 + 1
Answer:
(iv) 121 x4 – 198x3 – 183x2 + 216x + 144
Answer:
Question 2.
Find the square root of the expression
x2y2 – 10xy + 27 – 10yx + y2x2
Answer:
Question 3.
Find the values of a and b if the following polynomials are perfect squares.
(i) 4x4 – 12x3 + 37x2 + bx + a
Answer:
Since it is a perfect square
b + 42 = 0
b = – 42
a – 49 = 0
a = 49
∴ The value of a = 49 and b = – 42
(ii) ax4 + bx3 + 361x2 + 220x + 100
Answer:
Re-arrange the order we get
100 + 220x + 361x2 + bx3 + ax4
Since it is a perfect square
b – 264 = 0
b = 264
a – 144 = 0
a = 144
∴ The value of a = 144 and b = 264
Question 4.
Find the values of m and n if the following expressions are perfect sqaures.
(i) 1x4 – 6x3 + 13x2 + mx + n
Answer:
Since it is a perfect square
1x (m + 12) = 0
m + 12 = 0
m = -12
n – 4 = 0
n = 4
∴ The value of m = -12 and n = 4
(ii) x4 – 8x3 + mx2 + nx + 16
Answer:
Since it is a perfect square
m – 16 – 8 = 0
m – 24 = 0
m = 24
n + 32 = 0
n = -32
∴ The value of m = 24 and n = -32
