Question

find the values of m & n if the following polynomial is a perfect square 36x4 - 60x3+ 61x2;m+n​

Answer 1

Step-by-step explanation:

Find the square root of the following polynomials by division method

(i) x4 −12x3 + 42x2 −36x + 9

Step 1 :

x4 has been decomposed into two equal parts x2 and x2.

Step 2 :

Multiplying the quotient (x2) by 2, so we get 2x2. Now bring down the next two terms -12x3 and 42x2.

By dividing -12x3 by 2x2, we get -6x. By continuting in this way, we get the following steps.

Hence the square root of x4 −12x3 + 42x2 −36x + 9 is x2 - 6x + 3

(ii) 37x2 −28x3 + 4x4 + 42x + 9

Solution :

First let us arrange the given polynomial from greatest order to least order.

4x4 −28x3 + 37x2 + 42x + 9

Hence the square root of 37x2 −28x3 + 4x4 + 42x + 9 is 2x2 - 7x - 3.

(iii) 16x4 + 8x2 + 1

Solution :

Hence the square root of 37x2 −28x3 + 4x4 + 42x + 9 is 4x2 + 0x + 1.

(iv) 121x4 − 198x3 − 183x2 + 216x + 144

Solution :

Hence the square root of 121x4 − 198x3 − 183x2 + 216x + 144 is 11x2 + 9x + 12.

Question 2 :

Find the square root of the expression

(x2/y2) - 10x/y + 27 - (10y/x) + (y2/x2)

Solution :

By taking L.C.M, we get

(x4 - 10x3y + 27x2y2 - 10xy3+ y4)/x2y2

= √(x4 - 10x3y + 27x2y2 - 10xy3+ y4)/√x2y2

= (x2 - 5xy + y2)/xy

= (x/y) - 5 + (y/x)

Hence the square root of the polynomial (x2/y2) - 10x/y + 27 - (10y/x) + (y2/x2) is (x/y) - 5 + (y/x).

Let us look into the next example on "Finding the Square Root of a Polynomial by Long Division Method".

Finding the Missing Value in a Polynomial

Question 1 :

Find the values of a and b if the following polynomials are perfect squares

(i) 4x4 −12x3 + 37x2 + bx + a

Solution :