Let `a= cos((2pi)/7)+i sin((2pi)/7), A=a+a^2+a^4 and B=a^3+a^5+a^6, ` then A and B are the roots of the equation (A) `x^2-x+2=0` (B) `x^2-x-2=0` (C) `x^2+x+2=0` (D) none of these

The number of roots of the equation x^(3)+x^(2)+2x+sin x=0 in (-2 pi,2 pi)

The sum ofall the roots of the equation 6sin^(2)x+sin x-1=0 in x in[0,2 pi] is

Sum of roots of the equation x^(4)-2x^(2)sin^(2)(pi(x)/(2))+1=0 is 0(b)2(c)1 (d) 3

Find the number of roots of the equation x sin x = 1, x in [-2pi, 0) uu (0, 2pi] .

If x=(2)/(3) and x=-3 are the roots of the equation ax^(2)+7x+b=0, find the values of a and b.

Number of roots of the equation (3+cos x)^(2)=4-2sin^(8)x,x in[0,5 pi] are

Let p=cos(2 pi)/(7)+i sin(2 pi)/(7) . The complex number alpha=p+p^(2)+p^(4) and beta= p^3+p^5+p^6 are roots of the quadratic equation x^(2)+ax+b=0, where a and b are real. Then value of a, b

Number of real roots of the equation 2^x=2^(x-1)+2^(x-2)=7^x+7^(x-1)+7^(x-2) is (A) 4 (B) 2 (C) 1 (D) 0

The number of roots of the equation x sin x=1,x in[-2 pi,0)uu(0,2 pi] is 2(b)3 (c) 4 (d) 0

For the equation |x^(2)|+|x|-6=0, the sum of the real roots is 1( b) 0(c)2 (d) none of these