(x-2)quad [40.4x^(2)+40.0],[4.4x^(2)-4a^(2)x+(a^(4)-b^(4))=0],[2+5x-(a^(2)+a-6)=0]

solve for x:9x^(2)-6b^(2)x-(a^(4)-b^(4))=0

Solve the following quadratic for x: 4x^(2)-4a^(2)x+(a^(4)-b^(4))=0

int_(0)^(1)(x^(6)-4x^(5)+5x^(4)-4x^(2))dx

The equation whose roots are 0 , 0, 2, 2, -2, -2 is A) x^(6)+8x^(4)-16x^(2)=0 B) x^(6)-4x^(4)-16x^(2)=0 C) x^(6)-8x^(4)+16x^(2)=0 D) x^(6)+4x^(4)+16x^(2)=0

The biquadratic equation, two of whose roots are 1+i , 1-sqrt(2) is A) x^(4)-4x^(3)+5x^(2)-2x-2=0 B) x^(4)-4x^(3)-5x^(2)+2x+2=0 C) x^(4)+4x^(3)-5x^(2)+2x-2=0 D) x^(4)+4x^(3)+5x^(2)-2x+2=0

((x+4)/(x-4))^2-5((x+4)/(x-4))+6=0,(x!=4)

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

From the points (3,4), chords are drawn to the circle x^(2)+y^(2)-4x=0 .The locus of the midpoints of the chords is (a) x^(2)+y^(2)-5x-4y+6=0(b)x^(2)+y^(2)+5x-4y+6=0(c)x^(2)+y^(2)-5x+4y+6=0(d)x^(2)+y^(2)-5x-4y-6=0

Prove that, lim_(xtooo)(4x^(3)-5x^(2)+6x+9)/(3x^(4)+4x^(2)-11)=0