Question

For f(x) = a $x^2$ + bx + c, where a > 0 & a, b, c $ϵ$ R. The condition for both roots $\alpha$, $\beta$ of f(x) = 0 to lie in between two real values $x_1$ & $x_2$ is

• A. D ≥ 0, f(x₁) > 0, f(x₂) > 0
• B. x₁ < (-b/2a) < x₂
• C. x₁ > (-b/2a), x₂ > (-b/2a)
• D. Both a & b

Answer 1

The correct option is D

Both a & b

For f(x) = a + bx + c, where a > 0 & a, b, c $ϵ$ R. The conditions for both roots $\alpha$, $\beta$ of f(x) = 0 to lie in between two real values $x_1$ & $x_2$ is

D ≥ 0, f($x_1$) > 0, f($x_2$) > 0

$x_1$ < $\frac{(-b)}{2a}$ < $x_2$