If `2a+3b+6c=0`, show that the equation `ax^(2)+bx+c=0` has at least one root between 0 and 1.

If 2a+3b+6c=0 then the equation ax^2+bx+c=0 has in the interval (0,1)

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

If 27a+9b+3c+d=0 , then the equation 4ax^3+3bx^2+2cx+d=0 has at least one real root lying between

If 2a+3b+6c=0 " "(a, b, c in R) , then the quadratic equation ax^(2)+bx+c=0 has at least one root -

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 least one root in [0,1] (b) at least one root in [-1/2,1/2] (c) at least one root in [-1,0] (d) at least two roots in [0,2]

The roots of the equation ax^2+bx+c=0 are equal when-

If a, bin{1,2,3} and the equation ax^(2)+bx+1=0 has real roots, then

If 2a+3b+6c=0 (a,b,cinR) , then the quadratic equation ax^2+bx+c =0 has

If the equation a x^2+b x+c=0 has two positive and real roots, then prove that the equation a x^2+(b+6a)x+(c+3b)=0 has at least one positive real root.

IF b=c=0 then both roots of the equation ax^2+bx+c=0(ane0) are-