(C) Let $f(x) = ax^2+bx+c$. Since $a > 0$, the parabola opens upwards.Given that the roots $\alpha$ and $\beta$ satisfy $\alpha 2$,

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(C) Let $f(x) = ax^2+bx+c$. Since $a > 0$, the parabola opens upwards.Given that the roots $\alpha$ and $\beta$ satisfy $\alpha 2$, the value of the function at $x = -1$ must be negative because $-1$ lies between the roots $\alpha$ and $\beta$ (since $\alpha Thus, $f(-1) Substituting $x = -1$ into the quadratic expression, we get $f(-1) = a(-1)^2 + b(-1) + c = a - b + c$.Therefore, $a - b + c < 0$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Quadratic expressions and Position of roots

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If the quadratic equation $ax^2+bx+c=0$ $(a>0)$ has two roots $\alpha$ and $\beta$ such that $\alpha < -2$ and $\beta > 2$, then which of the following is true?

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A
$c < 0$
B
$a+b+c > 0$
C
$a-b+c < 0$
D
$a-b+c > 0$

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If the quadratic equation $ax^2+bx+c=0$ $(a>0)$ has two roots $\alpha$ and $\beta$ such that $\alpha < -2$ and $\beta > 2$, then which of the following is true?

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