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,depsilon R and f(x)=ax^3+bx^2-cx+d has local extrema at two points of opposite signs and abgt0 then roots of equation ax^2+bx+c=0 (A) are necessarily negative (B) have necessarily negative real parts (C) have necessarily positive real parts (D) are necessarily positive

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 roots of the equation ax^(2)+bx+c=0 are real and distinct,then

If a+b+c=0, then roots of the equation 3ax^(2)+4bx+5c=0 are (A) Positive (B) negative (C) Real and distinct (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

The expression ax^2+2bx+b has same sign as that of b for every real x, then the roots of equation bx^2+(b-c)x+b-c-a=0 are (A) real and equal (B) real and unequal (C) imaginary (D) none of these

If the roots of equation ax^(2)+bx+c=0;(a,b,c in R and a!=0) are non-real and a+c>b. Then