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 the chord of contact of the tangents from a point on the circle x^2 + y^2 = a^2 to the circle x^2 + y^2 = b^2 touch the circle x^2 +y^2 = c^2 , then the roots of the equation ax^2 + 2bx + c = 0 are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

If roots of the quadratic equation bx^(2)-2ax+a=0 are real and distinct then

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 ax^3+bx^2+cx+d has local extremum at two points of opposite signs then roots of equation ax^2+bx+c=0 are necessarily (A) rational (B) real and unequal (C) real and equal (D) imaginary

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

Prove that the roots of the quadratic equation ax^(2)-3bx-4a=0 are real and distinct for all real a and b,where a!=b.

The quadratic equation ax^(2)+bx+c=0 has real roots if: