If a + b + c > 9 c 4 and the equation a x 2 + 2 b x - 5 c = 0 has non-real complex roots, then

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Question: Answered & Verified by Expert

If

a + b + c > \frac{9 c}{4}

and the equation

{a x}^{2} + 2 b x - 5 c = 0

has non-real complex roots, then

MathematicsQuadratic EquationJEE Main

Options:

A $a > 0, c > 0$
B $a > 0, c < 0$
C $a < 0, c < 0$
D $a < 0, c > 0$

Solution:

2609 Upvotes Verified Answer

The correct answer is:

a > 0, c < 0

4 a + 4 b + 4 c - 9 c > 0

4 a + 4 b - 5 c > 0

f (x) = {a x}^{2} + 2 b x - 5 c, D < 0

f (2) = 4 a + 4 b - 5 c > 0

a > 0 and

\begin{array}{l} - 5 c > 0 \\ \Rightarrow c < 0 \end{array} \Rightarrow \begin{array}{l} a > 0 \\ c < 0 \end{array}

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