For what positive values of 'm', roots of the equation $x^{2} + m x + 4 = 0$ are distinct

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Solution

Consider the equation $x^{2} + m x + 4 = 0$
This is in the form $a x^{2} + b x + c = 0$ . The co-efficients are a = 1, b = m, c = 4
$△ = b^{2} - 4 a c, △ = m^{2} - 4 (1) (4), △ = m^{2} - 16$
If roots are distinct, then $△ > 0$
$∴ m^{2} - 16 > 0, m^{2} > 16, m > \sqrt{16} ∴ m > 4$

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