If \( \log _{2}\left(a x^{2}+x+a\right) \geq 1 \forall x \in R \), the

1.	If \( \log _{2}\left(a x^{2}+x+a\right) \geq 1 \forall x \in R \), then exhaustive set of values of ' \( a \) ' is:
Answer» log₂(ax²+x+a)>=1 => log_e(ax²+x+a)/log_e(2)>=1 => log_e(ax²+x+a)>=log(2) => ax²+x+a>=2 ax²+x+(a-2)>=0 a>0−(i) Δ≤0 1−4a(a−2)≤2 -1-4a²+8a<=0 1-8a+4a²>=0

If \( \log _{2}\left(a x^{2}+x+a\right) \geq 1 \forall x \in R \), then exhaustive set of values of ' \( a \) ' is:

Answer»

log₂(ax²+x+a)>=1

=> log_e(ax²+x+a)/log_e(2)>=1

=> log_e(ax²+x+a)>=log(2)

=> ax²+x+a>=2

ax²+x+(a-2)>=0

a>0−(i)

Δ≤0

1−4a(a−2)≤2

-1-4a²+8a<=0

1-8a+4a²>=0

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If \( \log _{2}\left(a x^{2}+x+a\right) \geq 1 \forall x \in R \), then exhaustive set of values of ' \( a \) ' is:

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