[" 8.(i) "2x^(2)-5x+3=0],[" (iii) "4x^(2)+4bx-(a^(2)-b^(2))=0],[" (v) "a^(2)x^(2)-3abx+2b^(2)=0]

(a+b)^(2)x^(2)-4abx-(a-b)^(2)=0

Without determining the roots of the following equations comment their nature: (i) 6sqrt3x^(2)-4x+sqrt3=0 (ii) 9a^(2)b^(2)x^(2)-48abcdx+64c^(2)d^(2)=0 (iii) a^(2)x^(2)+2abx=b^(2),a^(2)ne0 (iv) 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 (v) (b+c)x^(2)-(a+b+c)x+a=0

Without determining the roots of the following equations comment their nature: (i) 6sqrt3x^(2)-4x+sqrt3=0 (ii) 9a^(2)b^(2)x^(2)-48abcdx+64c^(2)d^(2)=0 (iii) a^(2)x^(2)+2abx=b^(2),a^(2)ne0 (iv) 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 (v) (b+c)x^(2)-(a+b+c)x+a=0

Find the values of k for which roots of the following equations are real and equal: (i) 12x^(2)+4kx+3=0 (ii) kx^(2)-5x+k=0 (iii) x^(2)+k(4x+k-1)+2=0 (iv) x^(2)-2(5+2k)x+3(7+10k)=0 (v) 5x^(2)-4x+2+k(4x^(2)-2x-1)=0 (vi) (k+1)x^(2)-2(k-1)x+1=0 (vii) x^(2)-(3k-1)x+2k^(2)+2k-11=0 (viii) 2(k-12)x^(2)+2(k-12)x+2=0

In each of the following,determine whether the given values are solutions of the given equation or not: 2x^(2)-x+9=x^(2)+4x+3,x=2,x=3 (ii) -sqrt(2)x-4=0,x=-sqrt(2),x=-2sqrt(2) (iii) a^(2)x^(2)-3abx+2b^(2)=0,x=a/b,x=b/a

Find the discriminant of each of the following equations: (i) 2x^(2)-7x+6=0" "(ii)" "3x^(2)-2x+8=0 (iii) 2x^(2)-5sqrt(2)x+4=0" "(iv)" "sqrt(3)x^(2)+2sqrt(2)x-2sqrt(3)=0 (v) (x-1)(2x-1)=0" "(vi)" "1-x=2x^(2)

Find the nature of the roots of the following quadratic equations: (i) 2x^(2)-8x+5=0" "(ii)" "3x^(2)-2sqrt(6)x+2=0 (iii) 5x^(2)-4x+1=0" "(iv)" "5x(x-2)+6=0 (v) 12x^(2)-4sqrt(15)x+5=0" "(vi)" "x^(2)-x+2=0

Find the centre and radius of each of the following circle : (i) x^(2)+y^(2)+4x-4y+1=0 (ii) 2x^(2)+2y^(2)-6x+6y+1=0 (iii) 2x^(2)+2y^(2)=3k(x+k) (iv) 3x^(2)+3y^(2)-5x-6y+4=0 (v) x^(2)+y^(2)-2ax-2by+a^(2)=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