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Online Quiz (Worksheet A B C D)

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High School Mathematics
6.14 Finding Square Root of The Method of Undetermined Coefficient

Example:
Find the square root of x4 - 4x3 + 8x2 - 8x + 4.
Solution:
The given expression being of degree four, its square root will be a quadratic expression. Therefore we may assume
x4 - 4x3 + 8x2 - 8x + 4 = (x + lx + m)2, where l and m are to be determined.
(x + lx + m)2 = (x + lx + m) (x + lx + m)
= x4 + lx3 + mx2 + lx3 + l2x2 + lmx + mx2 + lmx + m2
= x4 + 2lx3 + 2mx2 + l2x2 + 2lmx + m2
= x4 + 2lx3 + (l2 + 2m)x2 + 2lmx + m2
Thus,
x4 - 4x3 + 8x2 - 8x + 4 = x4 + 2lx3 + (l2 + 2m)x2 + 2lmx + m2
Comparing the coefficients of powers of x on either sides, we get
2l = -4, l2 + 2m = 8, 2lm = -8, m2 = 4
Therefore, l = -2 and m = 2.
Therefore, the square root is x2 + lx + m = x2 - 2x + 2.
Directions: Solve the following problems using above method. Also write at least 5 examples of your own.
Q 1: Find the square root of 4x4 + 12x3 + 17x2 + 2x + 4.
2x2 + 3x + 2
2x2 - 3x - 2
2x2 - 3x + 2
2x2 + 3x - 2

Q 2: Find the square root of 4x4 - 4x3 - 7x2 + 4x + 4
2x2 + x + 2
2x2 + x - 2
2x2 - x - 2
2x2 - x + 2

Q 3: Find the square root of 9x4 + 6x3 - 17x2 - 6x + 9.
3x2 + x - 3
3x2 - x - 3
3x2 - x + 3
3x2 + x + 3

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

Q 5: Find the square root of 16x4 - 24x3 - 23x2 + 24x + 16.
4x2 - 3x + 4
4x2 + 3x + 4
4x2 - 3x - 4
4x2 + 3x - 4

Q 6: Find the square root of 4x4 + 16x3 + 24x2 + 16x + 4.
2x2 + 4x - 2
2x2 - 4x + 2
2x2 - 4x - 2
2x2 + 4x + 2

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Question 8: This question is available to subscribers only!


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