Question

Determine the nature of roots of the following quadratic equation from their discriminant: 2x^2+5√3x+16=0​

Answer 1

$\huge \mathtt{ \fbox{Solution :)}}$

$\sf Given \: \begin{cases} \sf (i) \: The \: quadratic \: equation \: is \: 2 {(x)}^{2} + 5 \sqrt{3}x + 16 = 0 \\ \\ \sf (ii) \: Here \: a = 2 \: , \: b = 5 \sqrt{3} \: and \: c = 16\end{cases}$

We know that , the discriminant of quadratic equation is given by

$\mathtt{ \large\fbox{Discriminant = {(b)}^{2} - 4ac }}$

Substitute the known values , we get

$\sf \mapsto D = {(5 \sqrt{3} )}^{2} - 4 \times 2 \times 16 \\ \\ \sf \mapsto D = 25 \times 3 - 128 \\ \\ \sf \mapsto D = 75 - 128 \\ \\ \sf \mapsto D = - 53 < 0$

Hence , the given equation has no real roots i.e complex roots

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