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

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 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

If two distinct chords drawn from the point (a, b) on the circle x^2+y^2-ax-by=0 (where ab!=0) are bisected by the x-axis, then the roots of the quadratic equation bx^2 - ax + 2b = 0 are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

If two distinct chords drawn from the point (a, b) on the circle x^2+y^2-ax-by=0 (where ab!=0) are bisected by the x-axis, then the roots of the quadratic equation bx^2 - ax + 2b = 0 are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

If c>0 and the equation 3ax^(2)+4bx+c=0 has no real root,then

Consider a quadratic equation az^2 + bz + c =0 where a, b, c, are complex numbers. Find the condition that the equation has (i) one purely imaginary root (ii) one purely real root (iii) two purely imaginary roots (iv) two purely real roots

If a,b,c are real distinct numbers such that a ^(3) +b ^(3) +c ^(3)= 3abc, then the quadratic equation ax ^(2) +bx +c =0 has (a) Real roots (b) At least one negative root (c) Both roots are negative (d) Non real roots

(x^(2)+1)^(2)-x^(2)=0 has (i) four real roots (ii) two real roots (iii) no real roots (iv) one real root