If roots of `a x^2+b x+c=0` are `alphaa n dbetaa n d4a+2b+c >0,4a -2b+c >0,a n dc<0,` then possible values /values of `[alpha]+[beta]` is/are (where [.] represents greatest integer function) a.`-2` b.` -1 `c. `0 `d. `1`

If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^2 are the roots of a^2x^2+b^2x+c^2=0 , then a ,b ,c are in (A) G.P. (B) H.P. (C) A.P. (D) none of these

If alpha,beta are the roots of a x^2+b x+c=0,(a!=0) and alpha+delta,beta+delta are the roots of A x^2+B x+C=0,(A!=0) for some constant delta then prove that (b^2-4a c)/(a^2)=(B^2-4A C)/(A^2)

If alphaa n dbeta are the roots of ax^2+bx+c=0a n dS_n=alpha^n+beta^n, then a S_(n+1)+b S_n+c S_(n-1)=0 and hence find S_5dot

If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig a. c b. b c >0 c. a b >0 d. a b c<0

If sinthetaa n d-costheta are the roots of the equation a x^2-b x-c=0 , where a , ba n dc are the sides of a triangle ABC, then cosB is equal to 1-c/(2a) (b) 1-c/a 1+c/(c a) (d) 1+c/(3a)

If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are the roots of x^2-r x+s=0 , then the equation x^2-4q x+2q^2-r=0 has always. A. one positive and one negative root B . two positive roots C . two negative roots D . cannot say anything

If roots of equation x^2-2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

If both roots of the equation a x^2+x+c-a=0 are imaginary and c > -1, then a) 3a >2+4c b) 3a<2+4c c) c < a d) none of these

If the equation a x^2+b x+c=0(a >0) has two real roots alphaa n dbeta such that alphalt-2 and betagt2, then which of the following statements is/are true? (a) a-|b|+c<0 (b) clt0,b^2-4a cgt0 (c) 4a-2|b|+c<0 (d) 9a-3|b|+c<0

If sides of triangle A B C are a , ba n dc such that 2b=a+c then b/c >2/3 (b) b/c >1/3 b/c<2 (d) b/c<3/2