`2x^2-x-300=0` find the root

2x^(2)+6x+4=0 find the roots of equation.

If alpha and beta are the roots of x^(2)-x-2=0 , find the quadratic equation in x whose roots are (2alpha+1) and (2beta+1):

Find the value of roots of x^2-36=0 and then prove the root

Show that the equation 2x^(2)-6x+3=0 has real roots and find these roots.

If a and P are the roots of the equation x^2-11x + 24= 0 , find the equation having the roots a + 2 and P +2

If 3 is a root of the quadratic equation x^(2)-x+k=0 find the value of p so that the roots of the equation x^(2)+k(2x+k+2)+p=0 are equal.

If x=-2 is one of the roots of the quadratic equation x^(2)+x-2k=0, then find the value of k.

If a and b are the roots of the equation x^2-6x + 6=0 , find the value of 2(a^(2) + b^(2)) .

If -5 is a root of the quadratic equation 2x^(2)+px-5=0 and the quadratic equation p(x^(2)+x)+k=0 has equal roots, find the value of k.