If n and r are positive integers such that `0ltrltn` then roots of the equation `^nC_r x^2+2.^nC_(r+1)x+^nC_(r+2)=0` are necessarily (A) imaginary (B) real and equal (C) real and unequal (D) real but may be equal or unequal

If n and r are positive integers such that 0ltrltn then show that the roots of the quadratic equation nC_r x^2+2. ^nC_(r+1)x+^nC_(r+2)=0 are real.

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

Prove that "^nC_r + 2. ^nC_(r-1) + ^nC_(r-2) = ^(n+2)C_r

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,d are unequal positive numbes, then the roots of equation x/(x-a)+x/(x-b)+x/(x-c)+x+d=0 are necessarily (A) all real (B) all imaginary (C) two real and two imaginary roots (D) at least two real

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 roots of the equation x^(2)+2cx+ab=0 are real and unequal,then the roots of the equation x^(2)-2(a+b)x+(a^(2)+b^(2)+2c^(2))=0 are: (a) real and unequal (b) real and equal (c) imaginary (d) rational

If p,q, rin harmonic progression and p & r be different having same sign then the roots of the equation px^(2)+qx+r=0 are (A) real and equal(B) real and distinct (C) irrational (D) imaginary

If p, q, r are in H.P. and p and r be different having same sign then the , roots of the equation px^(2)+qx+r=0 are (A) Real and equal (B) Real and distinct (C) Irrational (D) Imaginary