[ 9.Let f(x)=ax+sin2x+b ,then f(x)=0 has (A) exactly one positive real root,if agt2 and blt0 (B) exactly one positive real root,if agt2 and bgt0 (C) Both(A)&(B) (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

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

Number of real roots of equation f(x)=0 is (A) 0 (B) 1 (C) 2 (D) none of these

Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha beta < 0 and f(alpha) f(beta) < 0 f . Then the equation f(x)=0 has three equal real roots one negative root if f(alpha) (a) 0 and f(beta) (b) one positive root if f(alpha) (c) 0 and f(beta) (d) none of these

Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha beta < 0 and f(alpha) f(beta) < 0 f . Then the equation f(x)=0 has three equal real roots one negative root if f(alpha) (a) 0 and f(beta) (b) one positive root if f(alpha) (c) 0 and f(beta) (d) none of these

The equation e^(sin x)-e^(-sin x)-4=0 has (A) infinite number of real roots (B) no real roots (C) exactly one real root (D) exactly four real roots

Let f(x)=x+2|x+1|+x-1| . If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 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 b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

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