Let $a > 0, b > 0,c >0 $ then both roots of the equation $ ax^2 + bx + c = 0$

Because all coefficients are strictly positive, the product of the roots c/a is positive and the sum of the roots -b/a is negative. This implies that if the roots are real, they must both be strictly negative. Furthermore, since the discriminant b^2 - 4ac could potentially be negative, the roots might be complex; in such a scenario, the complex roots would be conjugates with a real part equal to -b/(2a), which is also strictly negative. Therefore, regardless of whether the roots are real or complex, they must always have negative real parts.

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