Finding the Square Root of a Polynomial by Division Method
The long division method in finding the square root of a polynomial is useful when the degree of the polynomial is higher.
Find the square root of 64x4 − 16x3 + 17x 2 − 2x + 1
Before proceeding to find the square root of a polynomial, one has to ensure that the degrees of the variables are in descending or ascending order.
Example 3.22 Find the square root of the expression
If 9x4 + 12x3 + 28x2 + ax +b is a perfect square, find the values of a and b.
Because the given polynomial is a perfect square a − 16 = 0 , b − 16 = 0 Therefore a = 16 , b = 16 .