If `f(x)=x ` has non real roots, then the equation `f(f(x))=x` (A) has all real and unequal roots (B) has some real and non real roots (C) has all real and equal roots (D) has all non real roots

If a+b+c=0, then the equation 3ax^(2)+2bx+c=0 has (i) imaginary roots (ii) real and equal roots (ii) real and unequal roots (iv) rational roots

The equation e^(sinx)-e^(-sinx)-4=0 has (A) non real roots (B) integral roots (C) rational roots (D) real and unequal roots

Let f(x)=x^3+x^2+10x+7sinx, then the equation 1/(y-f(1))+2/(y-f(2))+3/(y-f(3))=0 has (A) no real root (B) one real roots (C) two real roots (D) more than two real roots

If 0ltalphaltbetaltgammaltpi/2 then the equation 1/(x-sinalpha)+1/(x-sinbeta)+1/(x-singamma)=0 has (A) imaginary roots (B) real and equal roots (C) real and unequal roots (D) rational roots

If the equation x^(2)-kx+1=0 has no real roots then

If f(x) is continuous in [0,2] and f(0)=f(2) then the equation f(x)=f(x+1) has (A) one real root in [0,2](B) atleast one real root in [0,1](C) atmost one real root in [0,2](D) atmost one real root in [1,2]

Suppose a, b, c are real numbers, and each of the equations x^(2)+2ax+b^(2)=0 and x^(2)+2bx+c^(2)=0 has two distinct real roots. Then the equation x^(2)+2cx+a^(2)=0 has - (A) Two distinct positive real roots (B) Two equal roots (C) One positive and one negative root (D) No real roots

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

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots.Then the equation p(p(x))=0 has A.only purely imaginary roots B.all real roots C.two real and purely imaginary roots D.neither real nor purely imaginary roots