If `a,b,c in R and a+b+c=0,` then the quadratic equation `3ax^2+2bx+c=0` has (a) at least one root in `[0, 1]` (b) at least one root in `[1,2]` (c) at least one root in `[3/2, 2]` (d) none of these

the quadratic equation 3ax^2 +2bx+c=0 has atleast one root between 0 and 1, if

Let a ,b , c in R such that no two of them are equal and satisfy |(2a, b, c),( b, c,2a), (c, 2a, b)|=0, then equation 24 a x^2+8b x+4c=0 has (a) at last one root in [0,1] (b) at last one root in [-1/2,1/2] (c) at last one root in [-1,0] (d) at last two roots in [0,2]

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have (a)no real solution (b)at least one real root in (-1,0) (c)at least one real root in (0,1) (d)none of these

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

If a ,b ,c in R^+a n d2b=a+c , then check the nature of roots of equation a x^2+2b x+c=0.

If a ,b ,c in Ra n da b c<0 , then equation b c x^2+2(b+c-a)x+a=0h a s (a)both positive roots (b)both negative roots (c)real roots (d)one positive and one negative root

If a ,b and c are in A.P. and one root of the equation a x^2+b c+c=0 is 2 , the find the other root dot

If a, b, c are in GP , then the equations ax^2 +2bx+c = 0 and dx^2 +2ex+f =0 have a common root if d/a , e/b , f/c are in