Let `f(x)=-ax^2-b|x|-c, -alpha le x lt 0, ax^2+b|x|+c 0 le x le alpha` where a,b,c are positive and `alpha gt 0`, then- Statement-1 : The equation f(x)=0has atleast one real root for `x in [-alpha,alpha]` Statement-2: Values of `f(-alpha) and f(alpha)` are opposite in sign.

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

If for some differentiable function f(alpha)=0 and f'(alpha)=0, Statement 1: Then sign of f(x) does not change in the neighbourhood of x=alpha Statement 2:alpha is repeated root of f(x)=0

Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha beta 0 (c)one positive root if f(alpha) 0 (d) none of these

If root of the equation x^(2) + ax + b = 0 are alpha , beta , then the roots of x^(2) + (2 alpha + a) x + alpha^(2) + a alpha + b = 0 are

Let f(x)=ax^3+bx^2+x+d has local extrema at x=alpha and beta such that alphabetalt0 and f(alpha).f(beta)gt0 . Then the equation f(x)=0 (A) has 3 distinct real roots (B) has only one real which is positive o a.f(alpha)lt0 (C) has only one real root, which is negative a.f(beta)gt0 (D) has 3 equal roots

Let f(x)=ax^(2)+bx+c , g(x)=ax^(2)+qx+r , where a , b , c , q , r in R and a lt 0 . If alpha , beta are the roots of f(x)=0 and alpha+delta , beta+delta are the roots of g(x)=0 , then

Let f(x)=ax^(2)+bx+c , g(x)=ax^(2)+qx+r , where a , b , c , q , r in R and a lt 0 . If alpha , beta are the roots of f(x)=0 and alpha+delta , beta+delta are the roots of g(x)=0 , then