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

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

The equation 3x^(2)+4ax+b=0 has atleast one root in (0, 1) if :

Statement-1: If a, b, c in R and 2a + 3b + 6c = 0 , then the equation ax^(2) + bx + c = 0 has at least one real root in (0, 1). Statement-2: If f(x) is a polynomial which assumes both positive and negative values, then it has at least one real root.

Statement-1: If a, b, c in R and 2a + 3b + 6c = 0 , then the equation ax^(2) + bx + c = 0 has at least one real root in (0, 1). Statement-2: If f(x) is a polynomial which assumes both positive and negative values, then it has at least one real root.

If a+b + c = 0, then show that the quadratic equation 3ax^(2) + 2bx +c=0 has at least one root in [0,1].

Statement I The equation 3x^(2)+4ax+b=0 has atleast one root in (o,1), if 3+4a=0. Statement II f(x)=3x^(2)+4x+b is continuos and differentiable in (0,1)

Statement I The equation 3x^(2)+4ax+b=0 has atleast one root in (o,1), if 3+4a=0. Statement II f(x)=3x^(2)+4x+b is continuos and differentiable in (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 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 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