`5 6 x ^ { 2 } + 2 x - 3 = 0 `

I. 5x^(2) + 2x - 3 = 0" "II. 2y^(2) + 7y + 6 = 0

Find the roots of the following quadratic equations i) 6sqrt5 x^(2) – 9x -3sqrt5 = 0 ii) x^(2) - x - 12 = 0 iii) 2x^(2) - 6x + 7 = 0 iv) 4x^(2) - 4x+17 = 3x^(2) -10x-17 v) x^(2) + 6x + 34 = 0 vi) 3x^(2) + 2x - 5 = 0

The equation of the diameter of the circle x^(2) + y^(2) -4x-6y +3 = 0 that is perpendicular 2x + 5y-6 = 0 is

The roots of 6x^(4) - 5x^(3) - 38x^(2) - 5x + 6 = 0 are

Show that the circles x^(2) + y^(2) + 2x = 0 and x^(2)+ y^(2) - 6 x -6 y + 2 = 0 touch externally at the point (1/5,3/5)

I. x ^(2) + 5x + 6 = 0 II. y^(2) + 3y +2 = 0

The root of x^(3) - 6x^(2) + 7x + 2 = 0 one root being 2 + sqrt(5) are