Show that the equation `2x^(2)-6x+7=0` has no real root.

By using the method of completing the square, show that the equation 4x^2+3x+5=0 has no real roots.

Show that the equation x^(2)+5x-6=0 has real roots.

Find the value of k for which the equation 3x^(2)-6x+k=0 has distinct and real root.

Show that the equation x^(3)+2x^(2)+x+5=0 has only one real root, such that [alpha]=-3 , where [x] denotes the integral point of x

Find the values of k for which the equation x^2+5k x+16=0 has no real roots.

If the equation x^(2)-x+ m^(2) = 0 has no real roots then m can satisfy

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has no real roots. Prove that in this case equation P(P(x))=x has no real roots either.

Find the least positive value of k for which the equation x^2+k x+4=0 has real roots.

Write the set of values of ' a ' for which the equation x^2+a x-1=0 has real roots.

Show that the equation x^2+a x-4=0 has real and distinct roots for all real values of a .