If `x_1, a n dx_2` are the roots of `x^2+(sintheta-1)x-1/2(cos^2theta)=0,` then find the maximum value of `x_1^2+x_2^2`

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

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

If x satisfies x^(2)-2x cos theta +1=0 , then the value of x^(n)+((1)/(x^n)) is

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

If (a^2-1)x^2+(a-1)x+a^2-4a+3=0 is identity in x , then find the value of a .

Find the roots of the equation (1)/(x)-(1)/(x-2)=3, x ne 0,2

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

If x_1a n dx_2 are the roots of the equation e^2*x^(lnx)=x^3 with x_1> x_2, then x_1=2x_2 (b) x_1=x_2^2 (c) 2x_1=x_2^2 (d) x_1^2=x_2^3

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