Let `x_1, x_2` are the roots of the quadratic equation `x^2+a x+b=0,w h e r ea ,b` are complex numbers and`y_1, y_2` are the roots of the quadratic equation `y^2+|a|y+|b|=0.` If `|x_1|=|x_2|=1,` then prove that `|y_1|=|y_2|=1`

Let x_(1),x_(2) are the roots of the quadratic equation x^(2) + ax + b=0 , where a,b, are complex numbers and y_(1), y_(2) are the roots of the quadratic equation y^(2) + |a|yy+ |b| = 0 . If |x_(1)| = |x_(2)|=1 , then prove that |y_(1)| = |y_(2)| =1

Let alpha,beta be the roots of the quadratic equation ax^2+bx+c=0 then the roots of the equation a(x+1)^2+b(x+1)(x-2)+c(x-2)^2=0 are:-

If p, q are the roots of the quadratic equation x2 + 2bx + c = 0, prove that 2log (√(y – p) + √(y – q)) = log2 + log(y + b + √(y2 + 2by + c))

If (x_1, y_1)&(x_2,y_2) are the ends of a diameter of a circle such that x_1&x_2 are the roots of the equation a x^2+b x+c=0 and y_1&y_2 are the roots of the equation p y^2=q y+c=0. Then the coordinates of the centre of the circle is: (b/(2a), q/(2p)) ( b/(2a), q/(2p)) (b/a , q/p) d. none of these

Solve the differential equation x^2dy+y(x+y)dx=0, given that y=1\ w h e n\ x=1.

Solve the differential equation x^2dy+y(x+y)dx=0, given that y=1\ w h e n\ x=1.

If y=e^(tan^-1x), prove that (1+x^2)y_2+(2x-1)y_1=0

If x_1, y_1 are the roots of x^2 +8x-97=0, x_2, y_2 are the roots of 4x^2 +32x-997=0 and x_3, y_3 are the roots of 9x^2 + 72x-9997=0 . Then the point (x_1, y_1), (x_2, y_2) and (x_3, y_3)

If the equation 2x+3y+1=0,3x+y-2=0, and a x+2y-b=0 are consistent, then prove that a-b=2.

If y=(sin^(-1)x)^2 , prove that (1-x^2)y_2-x y_1-2=0 .