Question

find the square root of the following polynomials by division method x⁴-12x³+42x²-36x+9​

Answer 1

Answer:

√x⁴-12x³+42x²-36x+9​ = x²-6x  + 3

Step-by-step explanation:

find the square root of the following polynomials by division method x⁴-12x³+42x²-36x+9​

  x⁴-12x³+42x²-36x+9​ = (x² + ax  + b)²

= x⁴ + 2ax³ + (2b + a²)x² + 2abx + b²

Comparing

2a = -12

=> a = -6

2b + a² = 42

=> 2b + 36 = 42

=> 2b = 6

=> b = 3

(x² -6x  + 3)²

  √x⁴-12x³+42x²-36x+9​ = x²-6x  + 3

Answer 2

therefore √x⁴-12x³+42x²-36x+9 = | x²-6x+3 |

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