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 (p,q) on the circle x^(2)+y^(2)=px+qy, where pq!=0 are bisected by x-axis then show that p^(2)gt8q^(2) .

If a,b are real, then the roots of the quadratic equation (a-b)x^(2)-5 (a+b) x-2(a-b) =0 are

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 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 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

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

If the roots of the equation x^2+2c x+a b=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 the roots of the equation ax^2 + bx + c = 0, a != 0 (a, b, c are real numbers), are imaginary and a + c < b, then

If a, b, c are positive and a = 2b + 3c, then roots of the equation ax^(2) + bx + c = 0 are real for

If a, b, c are real numbers satisfying the condition a+b+c=0 then the rots of the quadratic equation 3ax^2+5bx+7c=0 are