If `a,b, c epsilon R(a!=0)` and `a+2b+4c=0` then equatio `ax^(2)+bx+c=0` has

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 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

Statement -1 : The quadratic equation ax^(2)+bx+c=0 has real roots if (a+c)^(2) gt b^(2) , AA , a,b,c in R . and Statement -2 : The quadratic equation ax^(2) +bx+c=0 has real roots if b^(2) -4ac ge 0

If a, b and c are positive real and a = 2b + 3c , then the equation ax^(2) + bx + c = 0 has real roots for

a, b, c, in R, a ne 0 and the quadratic equation ax^(2) + bx + c = 0 has no real roots, then which one of the following is not true?

If a, b, c ∈ R, a ≠ 0 and the quadratic equation ax^2 + bx + c = 0 has no real root, then show that (a + b + c) c > 0

Let a, b and c be real numbers such that 4a + 2b + c = 0 and ab gt 0. Then the equation ax^(2) + bx + c = 0 has

If a, b, c are positive and a = 2b + 3c, then roots of the equation ax^(2) + bx + c = 0 are real for

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

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then