`a^(2)+12a+32`

Solve the quadratic equation x^(2) - 12x + 32 = 0 by completing square method :

If the circles x^(2) +y^(2) + ax -6y + 4 =0 and x^(2) + y^(2) - 12x + 32 =0 touch externally each other and if the distance between the centres is equal to 5, then the values of a are

Find the maximum or minimum values of the following expressions on R i) x^(2) + 6x – 27 ii) 3x^(2) + 2x + 7 iii) x^(2) - 12x + 32 iv) 2x^(2) + 3x + 1

Find the nature of the roots of the following equation, without finding the roots. x^(2)-12x+32=0

Factorise : (x-2y)^(2) - 12(x-2y) + 32

A common tangent to 9x^(2)+164;y^(2)-x+4=08x^(2)+y^(2)-12x+32=0

In the following questions two equation numbered I and II are given You have to solve both equations and . . . . . (i) x^(2)-7x+12=0 (ii) y^(2)-12y+32=0

Equation of common tangent of 9x^(2)+16y^(2)=144,y^(2)-x+4=0 and x^(2)+y^(2)-12x+32=0 is