Convert into perfect square. `(x^2+x+1/4)-1/4`

What is the first degree expression to be subtracted from x^(6)+8x^(4)+2x^(3)+16x^(2)+4x+5 in order to make it a perfect square? ( i -4x-4 (ii) 4x+4( iii) 4x-4( iv )-4x+4

If ax^2+bx+c=0 and px^2+qx+r=0 have one and only one root in common and a,b,c,p,q,r being rational, then b^2-ac and q^2-pr are 1) both are perfect squares 2) b^2-ac is a perfect square but q^2-pr is not a perfect square 3) q^2-pr is a perfect square but b^2-ac is not a perfect square 4) both are not perfect squares

STATEMENT-1 : The dual statement of "xis a perfect square or xis a prime number" is "x is a perfect square and a prime number and STATEMENT-2 : If x is a prime number, then it isnot a perfect square.

Discussion OF ex.-4.2 Solution OF a quadratic equation by completing the square method (1) make coefficient OF x^2 as 1 (2) Make coefficient x^2 as perfect square || Example 7,8,9,10,11,14,15 || Exemplar solved question

x^2+(2-k)x+k-(3)/(4) is a perfect square then k= (A) 3 (B) 1 (C) 7 (D) 5

If the expression x^(2)-(5m-2)x+(4m^(2)+10m+25) can be expressed as a perfect square then m is

If the largest real root of the equation x^(4)-4x^(3)+5x^(2)-4x+1=0 can be expressed as (a+sqrt(b))/(c) (where b does not contains any perfect square),then find the value of (a+b+c)

Consider the following numbers : 1. 2222 2. 11664 3. 343343 4. 220347 Which of the above are not perfect squares ?