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High School Mathematics
6.20 Square Roots of Algebraic Expressions Review - II

Square roots of Algebraic Expressions Review Test

Q 1: Solve, (x2 - x)2 - 8(x2 - x) + 12 = 0.
-1, -2, 2 and 3
-1, 2, -2 and -3
1, -2, 2 and 3

Q 2: Find the square root of x4 + 6x3 + 13x2 + 12x + 4.
x2 + 3x - 2
x2 - 3x - 2
x2 - 3x + 2
x2 + 3x + 2

Q 3: Expand, a2b. (Variables a, b, c and d)
a2b + d2a
a2b +b2c + c2d
b2c + c2d + d2a
a2b +b2c + c2d + d2a

Q 4: The difference of two symmetric expression is a ___________.
not a symmetric expression
symmetric expression

Q 5: 5x2 + 7y2 + 5z2, is this a homogeneous equation?
false
true

Q 6: Find the square root of 16x4 - 24x3 - 23x2 + 24x + 16.
4x2 + 3x + 4
4x2 + 3x - 4
4x2 - 3x + 4
4x2 - 3x - 4

Q 7: If one root of x2 - (5+a)x + 24 = 0 is 3 find the value of a.
4
5
2
6

Q 8: Find the square root of
(x2 + x - 30)(x2 + 8x + 12)(x2 - 3x - 10).
(x - 5)(x - 2)(x + 6)
(x - 5)(x + 2)(x + 6)
(x + 5)(x + 2)(x + 6)
(x - 5)(x + 2)(x - 6)

Q 9: Solve, x2 - 4x - 21 = 0.
3 and -7
-3 and -7
3 and 7
-3 and 7

Q 10: Find the square root of x2 + 4y2 + 9z2 + 4xy + 6xz + 12yz.
x + 2y + 3z
None of these
x +2y - 3z
x - 2y + 3z

Q 11: 3x4 - 5x3 + 3x2 - 4x2 + 5 = 0, is this reciprocal requation or not.
No
Yes

Q 12: Solve, 6x2 + 13x + 5 = 0.
5/3 and -1/2
-5/3 and -1/2
5/3 and 1/2
-5/3 and 1/2

Q 13: 5x4 + 6x3y + 3x2y2, is this homogeneous equation?
true
false

Q 14: Find the product of the roots of 2x2 + 7x + 6 = 0.
-3
3
2/5

Q 15: 2x4 - 3x3 + 5x2 - 3x + 2 = 0, is this reciprocal requation or not.
Yes
No

Q 16: Find the square root of
(x2 - 2x - 15)(x2 - 5x - 24)(x2 - 13x + 40).
(x - 8)(x - 5)(x + 3)
(x - 8)(x + 5)(x + 3)
(x + 8)(x - 5)(x + 3)
(x - 8)(x - 5)(x - 3)

Q 17: Find the square root of 961x2y4.
None of these
31xy2
31xy4
31x2y

Q 18: Solve, 3x2 - 4x - 6 = 0.
-2/3 and -3
2/3 and 3
-2/3 and 3
2/3 and -3

Q 19: Find the square root of 16x2 + 24xy + 9y2.
4x - 3y
4x + 3y
3x + 4y
None of these

Q 20: Solve, 6x4 - 35x3 + 62x2 - 35x + 6 = 0
None of these
3,1/2 and 1/3
2,1/2 and 1/3
2,3,1/2 and 1/3

Q 21: 3x3 + 4y3 + 5z3. is this a homogeneous equation?
false
true

Q 22: x2 + y2 + z2, is this equation symmetry or not?
No
Yes

Q 23: Find the square root of 625x6.
25x4
25x3
25x2

Q 24: 5x4 - 3x3 + 7x2 - 4x + 2 = 0, is this reciprocal requation or not.
Yes
No

Q 25: 5x + 3y+ 15y2, is this a homogeneous equation?
true
false

Q 26: Find the value of m and n so that x4 - 6x3 + 5x2 + mx + n is perfect square.
m = 8 and n = 6
m = 6 and n = 8
m = 12 and n = 4
m = 4 and n = 12

Q 27: Find the value of m and n so that x4 - 4x2 + mx + n is a perfect square.
m = 0 and n = 4
m = 2 and n = 3
m = 4 and n = 0
None of these

Q 28: Find the value of m and n so that 16x4 + 24x2 + mx + n is a perfect square.
m = 9 and n = 0
m = 3 and n = 4
m = 0 and n = 9
m = 4 and n = 3

Q 29: x3 + y3 + x2 + y2 + x + y, is this equation symmetry or not?
No
Yes

Q 30: 3x + 4y + 5, is this a homogeneous equation?
true
false

Q 31: Find the quadratic equation whose roots are 6 and 3.
x2 - 18x + 18
x2 - 9x + 18
x2 + 9x + 18
x2 - 9x + 9

Q 32: f(x) = 2x2 + 3x + 1, then f(3x) = _____.
18x2 + 9x + 1
18x2 - 9x + 1
18x2 + 9x + 3

Q 33: Find the quadratic equation whose roots are 8 and -3.
x2 + 5x - 24
x2 - 8x - 24
x2 - 11x - 24
x2 - 5x - 24

Q 34: What is the first degree expression to be added to x4 + 6x3 + 19x2 + 27x + 23.
2x + 3
2x + 4
2x - 4
3x + 2

Q 35: Find the square root of 4x4 + 12x3 + 17x2 + 2x + 4.
2x2 - 3x + 2
2x2 - 3x - 2
2x2 + 3x + 2
2x2 + 3x - 2

Q 36: Find the nature of the roots of the equation 3x2 - 12x + 7 = 0.
Real and distinct
Complex and distinct
Real and equal

Q 37: Find the square root of (x - 2y + 3z)2 - 12z(x-2y).
x - 2y - 3z
x - 2y - 2z
x - 3y - 3z

Q 38: Find the nature of the roots of the equation 2x2 - 3x + 7 = 0.
Real and equal
Real and distinct
Complex and distinct

Q 39: Find the value of a and b so that x4 - 6x3 + 5x2 + ax + b is a perfect square.
a = 8 and b = 7
a = 15 and b = 5
a = 12 and b = 4
a = 5 and b = 8

Q 40: Find the quadratic equation whose roots are 3/4 and 1/2.
8x2 - 10x - 3
8x2 - 8x + 3
8x2 + 10x + 3
8x2 - 10x + 3

Q 41: If one root of 3x2 - (10+a)x + 10 = 0 is 5 find the value of a.
7
5
4
6

Q 42: Find the product of the roots of 8x2 - 14x - 15 = 0.
15/8
8/15
-15/8
-8/15

Q 43: Solve, 6x2 + 9x - 6 = 0.
3/2 and 2/3
3/2 and -2/3
-3/2 and -2/3
-3/2 and 2/3

Q 44: If one root of 2x2 - (16+a)x + 25 = 0 is 5/2 find the value of a.
-2
-1
1
2

Q 45: Find the sum of the roots of 12x2 - x - 1 = 0.
-12
-1/12
12
1/12

Q 46: Find the square root of 1296x6y4.
36x2y3
36x3y2
36x4y

Q 47: Find the product of roots of the equation 3x2 + 7x + 6 = 0.
2
3
5
6

Q 48: If one root of 2x2 - (3+a)x + 6 = 0 is 2 find the value of a.
5
3
6
4

Q 49: Find the square root of
(6x2 + 16x + 8)(8x2 + 20x + 8)(12x2 + 14x + 4).
(3x + 2)(2x + 4)(3x + 3)
(4x + 2)(2x + 4)(4x + 3)
(3x + 2)(x + 4)(4x + 3)
(3x + 2)(2x + 4)(4x + 3)

Q 50: Find the nature of the roots of the equation x2 - 7x + 3 = 0.
Complex and distinct
Real and equal
Real and distinct

Q 51: Find the square root of (x + 2)(x + 4)(x + 6)(x + 8) + 16.
x2 + 8x + 20
x2 + 10x + 20
x2 + 10x + 15

Q 52: Solve, 12x2 - x - 1 = 0.
1/4 and -1/3
-1/4 and -1/3
-1/4 and 1/3
1/4 and 1/3

Q 53: x3 + 3x2y + xy2 + y3, is this equation symmetry or not?
Yes
No

Q 54: Square of the valiable x is _______.
x2
x2

Q 55: If one root of x2 - (4+a)x - 15 = 0 is -3 find the value of a.
-2
3
-3
2

Q 56: Find the square root of x4 - 6x3 + 5x2 + 12x + 4.
x2 - 3x - 2
x2 + 3x - 2
x2 - 3x + 2
x2 + 3x - 2

Q 57: Numbers of the form -6, -5 and -7 are called ________.
Real numbers
imaginary numbers

Q 58: x3 + y3 + x2 + y2 + x + y, is this symmetry or not.
No
Yes

Q 59: Find the square root of 25x4 - 20x2y2 + 4y4.
5x - 2y2
5x2 - 2y2
5x2 - 2y
5x - 2y

Q 60: Solve, 8x2 - 14x - 15 = 0.
-3/4 and -5/2
-3/4 and 5/2
3/4 and 5/2
3/4 and -5/2

Q 61: Find the nature of the roots of the equation 4x2 + 5x + 2 = 0.
Complex and distinct
Real and distinct
Real and equal

Q 62: Find the sum of roots of the equation 5x2 + 11x + 3 = 0.
11/5
-11/5
12/5
-12/5

Q 63: Solve, 6x2 + 7x + 2 = 0.
-1/2 and -2/3
1/2 and -2/3
1/2 and 2/3
-1/2 and 2/3

Q 64: Third degree homogeneous symmetric expression in x and y is _________.
ax3 + bx2y + cxy2 + dy3
ax2 + bx2y + cxy2 + dy2
ax3 + bx2y2 + cxy2 + dy3
ax3 + bx2y + cx2y2 + dy3

Q 65: Find the square root of
(12x2 + 23x + 10)(15x2 + 13x + 2)(20x2 + 29x + 5).
(4x + 5)(3x + 2)(5x + 1)
(4x + 5)(3x + 2)(5x + 2)
(4x + 5)(3x + 4)(5x + 1)
(4x + 3)(3x + 2)(5x + 1)

Q 66: Find the square root of 4x4 + y4 + 9z4 + 4x2y2 - 6y2z2 - 12x2z2.
2x2 + y + 3x2
2x + y + -3z
2x2 + y2 - 3z2

Q 67: Find the nature of the roots of the equation 3x2 - 7x + 3 = 0.
Real and distinct
Real and equal
Complex and distinct

Q 68: Expand, a2b. (Variables 'a' and 'b')
(a2b)(b2a)
a2b
(a2b)+(b2a)
b2a

Q 69: If one root of x2 - (7+a)x - 56 = 0 is -8 find the value of a.
6
8
-6
-8

Q 70: Find the value of ma nd n so that 25x4 + 50x2 + mx + n is a perfect square.
m = 0 and n = 5
m = 5 and n = 9
m = 0 and n = 25
None of these

Q 71: Find the square root of 25x2.
None of these
5x2
5x
15x

Q 72: Find the quadratic equation whose roots are 9 and 1/2.
2x2 - 19x + 9
2x2 + 19x + 9
2x2 - 14x + 9
2x2 - 19x - 9

Q 73: Solve, 6x4 - x2 - 2 = 0.
(-1/2) and (2/3)
(1/2) and (2/3)
(-1/2) and (-2/3)

Q 74: Solve, 2x2 + 13x + 15 = 0.
5/2 and 5
3/5 and -5
-3/2 and -5
-5/3 and 5

Q 75: Solve, 2x4 - 9x3 + 14x2 - 9x + 2 = 0
1,1/2 and 3/2
1,2 and 1/2
1,2 and 3/2
None of these

Q 76: How much is to be added to 4x4 - 12x3 - 11x2 + 30x + 21 to make it perfect square.
3
5
7
4

Q 77: Solve, 9x4 - 3x2 - 2 = 0.
(-1/3) and (-2/3)
(1/3) and (2/3)
(-1/3) and (2/3)

Q 78: Find the square root of 16x2y2z4.
4x2yz
4xy2z
4xyz2

Q 79: Find the square root of x4 - 4x3 + 8x2 - 8x + 4.
x2 + 2x + 2
x2 + 2x - 2
x2 - 2x - 2
x2 - 2x + 2

Q 80: Find the square root of 4x4 - 4x3 + 37x2 - 18x + 81
2x2 + x - 9
2x2 - x + 9
2x2 + x + 9

Q 81: Find the value of a and b so that 9x4 + 6x3 - 17x2 - ax + b is a perfect square.
a = 9 and b = 6
a = 7 and b = 8
a = 8 and b = 7
a = 6 and b = 9

Q 82: Find the quadratic equation whose roots are 3/2 and 5/2.
4x2 - 16x + 15
4x2 - 16x + 15
4x2 + 16x + 15
4x2 - 12x + 15

Q 83: 3x3 - 6x2y + 3xy2 + 7y3, is this a homogeneous equation?
true
false

Q 84: Find the sum of the roots of 6x2 + 13x + 5 = 0.
6/13
-6/13
13/6
-13/6

Q 85: Find the square root of
(x2 - 4x + 3)(x2 - 12x + 27)(x2 - 10x + 9).
(x - 9)(x - 3)(x + 1)
(x - 9)(x - 3)(x - 1)
(x + 9)(x - 3)(x - 1)
(x - 9)(x + 3)(x - 1)

Q 86: First degree homogeneous expression in x and y is _____.
ac * by
ax + by

Q 87: Solve, (2x2 - 3x)2 - 4(2x2 - 3x) - 5 = 0.
1, 1, 1/2 and 5/2
-1, 1, 1/2 and 5/2
-1, 1, -1/2 and 5/2

Q 88: What is the first degree expression to be added to x4 + 4x3 - 4x2 - 19x + 11 = 0 to make it perfect square.
3x + 6
3x - 6
3x - 5
3x + 5

Q 89: f(x) = 2x2 - 4x + 1, then 3f(x) = _______.
6x2 - 12x + 1
6x2 - 12x + 3
2x2 - 4x + 3
6x2 - 4x + 3

Q 90: Solve, x2 - 11x + 28 = 0.
-4 and 7
4 and -7
4 and 7
-4 and -7

Q 91: Find the square root of x4 - 2x3 - 5x2 + 6x + 9.
x2 - x - 3
x2 - x + 3
x2 + x - 3

Q 92: Find the square root of
(x2 + 10x + 16)(x2 + 11x + 24)(x2 + 5x + 6).
(x + 2)(x + 8)(x + 3)
(x + 2)(x - 8)(x + 3)
(x - 2)(x + 8)(x + 3)
(x + 2)(x + 8)(x - 3)

Q 93: The sum of two symmetric expression is a _______.
not a symmetric expression
symmetric expression

Q 94: Find the square root of x4 + y4 + 9z4 - 2x2y2 - 6x2z2 + 6y2z2.
x2 - y2 + 3z2
x2 + y2 + 3z2
x2 - y2 - 3z2

Q 95: Find the nature of the roots of the equation 3x2 - 15x + 5 = 0.
Real and distinct
Real and equal
Complex and distinct

Q 96: Solve, 6x4 + 11x2 - 3 = 0.
(-3/2) and (--1/3)
(3/2) and (-1/3)
(-3/2) and (-1/3)

Q 97: Solve, 12x4 + 10x2 + 2 = 0
(-1/2) and (-1/3)
(-1/2) and (--1/3)
(1/2) and (-1/3)

Q 98: Product of two homogeneous expression is a ________.
homogeneous expression
not a homogeneous expression

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Question 100: This question is available to subscribers only!


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