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

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].

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

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

If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one real lying in the interval

If the equation ax^(2) + 2 bx - 3c = 0 has no real roots and (3c)/(4) lt a + b , then

If a, b, c, d are real numbers such that (a+2c)/(b+3d)+(4)/(3)=0 . Prove that the equation ax^(3)+bx^(2)+cx+d=0 has atleast one real root in (0, 1).

Let a,b,c be nonzero real numbers such that int_(0)^(1)(1+cos^(8)x)(ax^(2)+bx+c)dx=int_(0)^(2)(1+cos^(8)x)(ax^(2)+bx+c)dx=0 Then show that the equation ax^(2)+bx+c=0 will have one root between 0and 1 and other root between 1 and 2.