Find the values of a if `x^2-2(a-1)x+(2a+1)=0` has positive roots.

Find the value of a if the equation 2x^2-(a+1)x+(a-1)=0 has equal roots.

Find the value of k if 9x^2 + kx +1=0 has equal roots.

Find the roots of -x^(2) + x-2=0

Find the value of int_0^1 2x^3-3x^2-x+1 3dxdot

Number of integral values of a for which the equation x^2-(a+1)x+a-1=0 , has integral roots, is equal to -

Find the values of k so that the equation x^(2)-2x(1+3k)+7(3+2k)=0 has real and equal roots.

If int_0^1e^-(x^2)dx=a , then find the value of int_0^1x^2e^-(x^2)dx in terms of a .

Find the roots of x^(2) + x + 1/sqrt(2)=0

Find the roots of x^(2) + x/sqrt(2)+1=0

If (x^(+(1)/(2)) + x^(-(1)/(2)))^(2) = (9)/(2) , then find the value of (x^((1)/(2))-x^(-(1)/(2))) for x gt 1 .