Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

#### Online Quiz (WorksheetABCD)

Questions Per Quiz = 2 4 6 8 10

### High School Mathematics6.14 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 - 22x2 + 3x + 22x2 - 3x - 22x2 - 3x + 2 Q 2: Find the square root of x4 - 6x3 + 5x2 + 12x + 4.x2 + 3x - 2x2 - 3x + 2x2 + 3x - 2x2 - 3x - 2 Q 3: Find the square root of 16x4 - 24x3 - 23x2 + 24x + 16.4x2 + 3x + 44x2 + 3x - 44x2 - 3x + 44x2 - 3x - 4 Q 4: Find the square root of 9x4 + 6x3 - 17x2 - 6x + 9.3x2 - x - 33x2 + x + 33x2 - x + 33x2 + x - 3 Q 5: Find the square root of 4x4 + 16x3 + 24x2 + 16x + 4.2x2 + 4x + 22x2 - 4x + 22x2 + 4x - 22x2 - 4x - 2 Q 6: Find the square root of x4 - 4x3 + 8x2 - 8x + 4.x2 - 2x + 2x2 + 2x - 2x2 - 2x - 2x2 + 2x + 2 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!