Determine the nature of roots of the following equation from the discriminant: `y ^2 −5y+11=0`

Determine the nature of the roots of the following quadratic equations: 2x^2+x-1=0 x^2-4x+4=0 x^2+x+1=0 4x^2-4x+1=0 2x^2+5x+5=0

Write the discriminant of the following equation : x ^2−4x+2=0

Find the nature of the roots of the following equation, without finding the roots. 2x^(2)-8x+3=0

Find the nature of the roots of the following equation, without finding the roots. 9x^(2)-30x+25=0

Determine the value of k so that the following linear equations have no solution: (3k+1)x+3y-2=0,\ \ \ \ (k^2+1)x+(k-2)y-5=0

Write the discriminate of each of the following quadratic equation: 2x ^2+4x+5=0

Determine the values of a and b so that the following system of linear equations have infinitely many solutions: (2a-1)x+3y-5=0,\ \ \ \ 3x+(b-1)y-2=0

Determine the values of m and n so that the following system of linear equations have infinite number of solutions: (2m-1)x+3y-5=0 . 3x+(n-1)y-2=0

Determine the order and degree of the following differential equation. State also whether they are linear or non-linear: (d^2y)/(dx^2)+4y=0