17.) α2-1, b are in A.P., a, β1" β2, , β2n 1, b are in GP and a, γ1-Y2, 1, b are in HP, where If a, α1, α2, b are positive, then the equation α, X2-A, x + yn = 0 has (A) real and equal roots (C) imaginary roots y (B) real and unequal roots (D) roots which are in A.P

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

If a,b,c are in GP,where a,are positive,then the equation ax^(2)+bx+c=0 has (a) real roots (b) imaginary roots c) ratio of roots =1:w where w is a nonreal cube root of unity (d) ratio of roots =b:ac

If a, a_1 ,a_2----a_(2n-1),b are in A.P and a,b_1,b_2-----b_(2n-1),b are in G.P and a,c_1,c_2----c_(2n-1),b are in H.P (which are non-zero and a,b are positive real numbers), then the roots of the equation a_nx^2-b_nx |c_n=0 are (a) real and unequal (b) real and equal (c) imaginary (d) none of these

If a,b,c are rational and are in G.P and a-b, c-a, b-c are in H.P. then the equations ax^2+4bx-c=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0 have (A) imaginary roots (B) irrational roots (C) rational roots (D) a common root

If a, b, c are rational and the tangent to the parabola y^2 = 4kx , at P(p, q) and Q(q, b) meet at R(r, c) , then the equation ax^2 + bx-2c=0 has (A) imaginary roots (B) real and equal roots (C) rational roots (D) irrational roots

If roots of the equation a x^2+b x+c=0 be a quadratic equation and α,β are its roots then f(−x)=0 is an equation whose roots

If roots of the equation a x^2+b x+c=0 be a quadratic equation and α,β are its roots then f(−x)=0 is an equation whose 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 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