Let `a , b , c` be three real numbers such that `a

Let a, b, c be non-zero real numbers such that ; int_0^1 (1 + cos^8 x)(ax^2 + bx + c)dx = int_0^2 (1+cos^8 x)(ax^2 + bx +c)dx then the quadratic equation ax^2 + bx + c = 0 has -

Let a ,\ b ,\ c be three non-zero real numbers such that the equation sqrt(3)\ acosx+2\ bsinx=c ,\ x in [-pi/2,pi/2] , has two distinct real roots alpha and beta with alpha+beta=pi/3 . Then, the value of b/a is _______.

Let a ,b and c be real numbers such that a+2b+c=4 . Find the maximum value of (a b+b c+c a)dot

Let a, b and c be real numbers such that 4a + 2b + c = 0 and ab gt 0. Then the equation ax^(2) + bx + c = 0 has

Let a and b be two real numbers such that a > 1, b > 1. If A=[(a,0), (0,b)] , then lim_(n to oo) A^(-n) is a. unit matrix b. null matrix c. 2l d. none of these

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] Let omega be a solution of x^3-1=0 with Im(omega)gt0. I fa=2 with b nd c satisfying (E) then the vlaue of 3/omega^a+1/omega^b+3/omega^c is equa to (A) -2 (B) 2 (C) 3 (D) -3

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] Let b=6, with a and c satisfying (E). If alpha and beta are the roots of the quadratic equation ax^2+bx+c=0 then sum_(n=0)^oo (1/alpha+1/beta)^n is (A) 6 (B) 7 (C) 6/7 (D) oo

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] If the point P(a,b,c) with reference to (E), lies on the plane 2x+y+z=1 , the the value of 7a+b+c is (A) 0 (B) 12 (C) 7 (D) 6

Let a,b and c be real numbers such that 4a+2b+c=0 and ab lt 0 .Then the equation ax^2+bx+c=0 .

Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then the sum of all possible values of |a-d|=