If `2a+3b+6c=0,` then prove that at least one root of the equation `a x^2+b x+c=0` lies in the interval (0,1).

If 2a+3b+6c=0, then prove that at least one root of the equation ax^(2)+bx+c=0 lies in the interval (0,1) .

One root of the equation cosx-x+1/2=0 lies in the interval

If 2a+3b+6c=0 , then at least one root of the eqution ax^2+bx+c=0 lies in the interval

If 2a + 3b + 6c = 0, show that there exists at least one root of the equation ax^(2) + bx + c = 0 in the interval (0,1).

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

If a , b , c , are real number such that a c!=0, then show that at least one of the equations a x^2+b x+c=0 and -a x^2+b x+c=0 has real roots.

Consider the quadratic equation (c-3) x^2 - 2cx + (c - 2) = 0 , c ne 3 . Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is: