If `3(a+2c)=4(b+3d),` then the equation `a x^3+b x^2+c x+d=0` will have no real solution at least one real root in `(-1,0)` at least one real root in `(0,1)` none of these

If a+b+2c=0, c!=0, then equation ax^2+bx+c=0 has (A) at least one root in (0,1) (B) at least one root in (0,2) (C) at least on root in (-1,1) (D) none of these

If the equation ax^(2)+bx+c=x has no real roots,then the equation a(ax^(2)+bx+c)^(2)+b(ax^(2)+bx+c)+c=x will have a.four real roots b.no real root c.at least two least roots d.none of these

If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^(2)+2bx+c=0 has (a) at least one root in [0,1] (b) at least one root in [1,2](c) at least one root in [(3)/(2),2] (d) none of these

Let f(x)= 3/(x-2)+4/(x-3)+5/(x-4) . Then f(x)=0 has (A) exactly one real root in (2,3) (B) exactly one real root in (3,4) (C) at least one real root in (2,3) (D) none of these

If a,b,c in R and (a+c)^(2)

If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

If f(x) is continuous in [0,2] and f(0)=f(2) then the equation f(x)=f(x+1) has (A) one real root in [0,2](B) atleast one real root in [0,1](C) atmost one real root in [0,2](D) atmost one real root in [1,2]

If a,b,c,d in R, then the equation (x^(2)+ax-3b)(x^(2)-cx+b)(x^(2)-dx+2b)=0 has a.6 real roots b.at least 2 real roots c.4 real roots d.none of these

Find the condition if the equation 3x^(2)+4ax+b=0 has at least one root in (0,1).

If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one real lying in the interval