f(x)=ax^2-bx-a is a quadratic expression. If | vedclass

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(C) Given $f(x)=ax^2-bx-a$ is a quadratic expression such that $f(x) \leq K, \forall x \in R$. This implies $ax^2-bx-a-K \leq 0, \forall x \in R$. For

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$K > 0$

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(C) Given $f(x)=ax^2-bx-a$ is a quadratic expression such that $f(x) \leq K, \forall x \in R$. This implies $ax^2-bx-a-K \leq 0, \forall x \in R$. For a quadratic expression $Ax^2+Bx+C$ to be less than or equal to $0$ for all $x$,the coefficient of $x^2$ must be negative $(a Here,$D = (-b)^2 - 4(a)(-a-K) \leq 0$. $b^2 + 4a(a+K) \leq 0$. $b^2 + 4a^2 + 4aK \leq 0$. Since $b^2 + 4a^2 \geq 0$,for the expression to be $\leq 0$,$4aK$ must be negative. Given $a Thus,$K > 0$.

$f(x)=ax^2-bx-a$ is a quadratic expression. If $K$ is the least real number such that $f(x) \leq K, \forall x \in R$,then

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