`3x^2-4sqrt3x+4=0`

Determine the nature of the roots of the following quadratic equations: (i) 3x^2-4sqrt(3)x+4=0 (ii) 3x^2-2sqrt(6)x+2=0 (iii) (x-2a)(x-2b)=4a b

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i) 2x^2-3x+5=0 (ii) 3x^2-4sqrt(3)x+4=0 (iii) 2x^2-6x+3=0

Determine the nature of roots of the following quadratic equations: (i) 2x^(2)+5x-4=0 (ii) 9x^(2)-6x+1=0 (iii) 3x^(2)+4x+2=0 (iv) x^(2)+2sqrt2x+1=0 (v) x^(2)+x+1=0 (vi) x^(2)+ax-4=0 (vii) 3x^(2)+7x+(1)/(2)=0 (viii) 3x^(2)-4sqrt3x+4=0 (ix) 2sqrt3x^(2)-5x+sqrt3=0 (x) (x-2a)(x-2b)=4ab

Solve the following quadratic equation : 4sqrt3x^(2)+5x-2sqrt3=0

Find the roots of the quadratic equations by applying the quadratic formula. (i) 2x^2 -7x+3 =0 (ii) 2x^2+x-4 =0 (iii) 4x^2+4sqrt3x+3=0 (iv) 2x^2+x+4 = 0

The lines represented by the equation x^2 + 2sqrt(3)xy + 3y^(2) -3x -3sqrt(3)y -4=0 , are

Solved the following equation by the method of completing the square : 4sqrt3x^(2)+5x-2sqrt3=0

The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 t= 0 & sqrt3 tx +ty-4 sqrt3=0 (where t is a parameter) is a hyperbola whose eccentricity is: (a) sqrt3 (b) 2 (c) 2/sqrt3 (d) 4/3

The locus of the point of intersection of lines sqrt3x-y-4sqrt(3k) =0 and sqrt3kx+ky-4sqrt3=0 for different value of k is a hyperbola whose eccentricity is 2.

In each of the following, determine whether the given values are solutions of the given equation or not: (i) x^2-3x+2=0,\ \ x=2,\ x=-1 (ii) x^2+x+1=0,\ \ x=0,\ x=1 (iii) x^2-3sqrt(3)x+6=0,\ \ x=sqrt(3),\ \ x=-2sqrt(3) (iv) x+1/x=(13)/6,\ \ x=5/6,\ \ x=4/3