Find the roots of given equation `2y ^2−y−1=0`

The equation of the circle whose one diameter is PQ, where the ordinates of P, Q are the roots of the equation x^(2)+2x-3=0 and the abscissae are the roots of the equation y^(2)+4y-12=0 is

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

Let alpha and beta be the roots of the equation x^(2) + x + 1 = 0 . Then, for y ne 0 in R. [{:(y+1, alpha,beta), (alpha, y+beta, 1),(beta, 1, y+alpha):}] is

Find the values of m for which the equation 3x^(2)+mx+2=0 has equal roots. Also, find the roots of the given equation.

Find the equation whose roots are (1)/(4) times of the roots of the equation x^(2)-3x+2=0

Find the value of x and y in given equations x+2y+3=0 and 4x-5y+1=0 .

Find the set of all solutions of the equation 2^|y| -|2^(y -1) -1| = 2^(y -1) +1

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

If 1 is a common root of the equations ay^2+ay+3=0 and y^2+y+b=0 ,then find the value of ab.

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