`0.1^(4x^(2)-2x-2)<=0.1^(2x-3)`

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

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

If points A and B are (1,0) and (0,1) respectively,and point C is on the circle x^(2)+y^(2)=1, then the locus of the orthocentre of triangle ABC is x^(2)+y^(2)=4x^(2)+y^(2)-x-y=0x^(2)+y^(2)-2x-2y+1=0x^(2)+y^(2)+2x-2y+1=0

If the product of the roots of 5x^(2)-4x+2+m(4x^(2)-2x-1)=0 is 3, then m=

If x^(4)-4x^(3)+2x^(2)-4x+1=0 then x is

The value of int_(0)^(2)((x^(2)-2x+4)sin(x-1))/(2x^(2)-4x+5)dx is equal to

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x. The locus of the midpoint of PQ is y^(2)+4x+2=0y^(2)-4x+2=0x^(2)-4y+2=0x^(2)+4y+2=0

The radical centre of the circles x^(2)+y^(2)=9 , x^(2)+y^(2)-2x-2y-5=0 , x^(2)+y^(2)+4x+6y-19=0 is A) (0,0) (B) (1,1) (C) (2,2) (D) (3,3)

Solve the equation x^(4)+4x^(3)+5x^(2)+2x-2=0, one root being -1+sqrt(-1)