Let f(x) = ax2 + bx + c is a quadratic polynomial. If 3 a + \sqrt{3} b + c = 1 and 4a + 2b + c = 0, then which of the following may be possible? (a, b, c \in R)

Engineering

Mathematics

Graph of Quadratic Expression and Properties

Question

Let f(x) = ax² + bx + c is a quadratic polynomial. If $3 a + \sqrt{3} b + c = 1$ and 4a + 2b + c = 0, then which of the following may be possible? (a, b, c $\in$ R)

b² – 4ac < 0

$c = - 4 + 2 \sqrt{3}$

b² – 4ac = 0

b² – 4ac > 0

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