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$If f (x) = a x^{2} + b x + c and f (- 1) \geq - 4, f (1) \leq 0 and f (3) \geq 5, then the least value of a is$

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Correct option is B

f(−1)≥−4----(1)⇒a−b+c≥−4f(1)≤0⇒a+b+c≤0⇒ −a−b−c≥0---(2)f(3)≥5 and 9a+3b+c≥5----(3) From (i) + (ii) ⇒−2b≥−4----(4) From (ii) +(iii)+(iv)⇒8a≥1 ⇒ a≥1/8

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If f(x)=ax2+bx+c and f(−1)≥−4,f(1)≤0 and f(3)≥5, then the least value of a is

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Ready to Test Your Skills?

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$If f (x) = a x^{2} + b x + c and f (- 1) \geq - 4, f (1) \leq 0 and f (3) \geq 5, then the least value of a is$