Question

If a > 0 , then the minimum value of ax^ 2 +bx+c at^ x= -b 2a is​

Answer 1

Step-by-step explanation:

Let f(x) = ax2 + bx + 8. Since f(x) = 0 does not have 2 distinct real roots, hence we have either f(x) ≥ 0 ∀ x ∈ R or f (x) ≤ 0 ∀ x ∈ R. Since f(0) = 8, therefore ⇒ f(x) ≥ 0 ∀ x ∈ R In particular, f(2) ≥ 0 ⇒ 4a + 2b + 8 ≥ 0 ⇒ 2a + b ≥ − 4 Hence, the minimum value is −4