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 f(x)=ax^3+bx^2+cx+d has local extrema at two points of opposite signs than prove that roods of the quadratic ax^2+bx+c=0 are real and distinct.

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

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

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

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