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

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

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

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 ax^(2)+bx+c=0 has real roots if:

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

The quadratic equation ax^(2)+5bx+2c=0 has equal, roots 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.

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