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`

The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (where [.] represents the greatest integer function). -1 (b) 1 (c) 0 (d) none of these

If alphaa n dbeta are roots of the quadratic equation a x^2+b x+c=0 and a+b+c >0,a-b+c >0&c<0,t h e n[alpha]+[beta] is equal to (where [dot] denotes the greatest integer function) (a) 10 (b) -3 (c) -1 (d) 0

If A , B , C are three real numbers and p=[A+B+C] and q=[A]+[B]+[C]dot (where [.] represents greatest integer function). Then maximum value of [p-q] is: 1 (b) 0 (c) 2 (d) 3

Consider a quadratic equation ax^2 + bx + c = 0 having roots alpha, beta . If 4a + 2b + c > 0,a-b+c 0 then |[alpha] + [beta]| can be {where [] is greatest integer}

If a+b+3c=1 and a gt 0, b gt 0, c gt 0 , then the greratest value of a^(2)b^(2)c^(2) is

Let A(−4,0) , B(4,0) & C(x,y) be points on the circle x^2 + y^2 = 16 such that the number of points for which the area of the triangle whose vertices are A, B and C is a positive integer, is N then the value of [N/7] is, where [⋅] represents greatest integer function.

If a, b, c are real if ax^(2)+ bx + c = 0 has two real roots alpha, beta where a lt -1, beta gt 1 then

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

If 2a+b+3c=1 and a gt 0, b gt 0, c gt 0 , then the greatest value of a^(4)b^(2)c^(2)"_____" .