Let f(x) = ax2 + 2bx – 3c has no real root and \frac{3 c}{4}

Engineering

Mathematics

Graph of Quadratic Expression and Properties

Question

Let f(x) = ax² + 2bx – 3c has no real root and $\frac{3 c}{4}$ < a + b, then

$a + | b | > \frac{3 c}{4}$

c < 0

b < 0

a > 0

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4a + 4b – 3c > 0 → f(2) > 0

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