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`

The roots of the quadratic equation 2x^2+3x+1 =0 are

The roots of the quadratic equation x^(2)-2x+1=0 are ______ and _____.

If a in (-1,1), then roots of the quadratic equation (a-1)x^2+a x+sqrt(1-a^2)=0 are

If one of the roots of the quadratic equation be x^2 - (1+b)x+6 = 0 be 2, then find the other root.

If the roots of the equation x^2-2px+q=0 are equal and ylt0 and pne1 , show that the roots of the equation (1+y)x^2-2(p+y)x+q+y=0 are real and unequal.

Prove that the quadratic equation 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 will have no real root if aneb .

If m_1 and m_2 are the roots of the equation x^2-a x-a-1=0 , then the area of the triangle formed by the three straight lines y=m_1x ,y=m_2x , and y=a(a!=-1) is

The solution of the equation (x^2y+x^2)dx+y^2(x-1)dy=0 is given by

The x-coordinates of the vertices of a square of unit area are the roots of the equation x^2-3|x|+2=0 . The y-coordinates of the vertices are the roots of the equation y^2-3y+2=0. Then the possible vertices of the square is/are (a)(1,1),(2,1),(2,2),(1,2) (b)(-1,1),(-2,1),(-2,2),(-1,2) (c)(2,1),(1,-1),(1,2),(2,2) (d)(-2,1),(-1,-1),(-1,2),(-2,2)

If alphabeta the roots of the equation x^2-x-1=0 , then the quadratic equation whose roots are (1 + alpha)/(2 -alpha),(1 + beta)/(2 - beta)