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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Let's calculate its discriminant ~

[tex]\qquad \sf  \dashrightarrow \: {t}^{2} + \cfrac{17}{2} t - 5 = 0[/tex]

[ Multiply both sides by 2 ]

[tex]\qquad \sf  \dashrightarrow \: 2 {t}^{2} + 17t - 10[/tex]

  • a = 2

  • b = 17

  • c = 10

[tex]\qquad \sf  \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (17) {}^{2} - (4 \times 2 \times - 10)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 289 - ( - 80)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 369[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt {d }= 3 \sqrt{41} \approx19.209 [/tex]

So, by quadratic formula :

[tex]\qquad \sf  \dashrightarrow \: t = \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: t = \dfrac{ - {17}^{} \pm \sqrt{369} }{2 \times 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \:t = \cfrac{ - 17 - 19.209}{4} \: \: and \: \: t = \dfrac{-17+19.209}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \:t = \cfrac{ - 36.209}{4} \: \: and \: \: t = \dfrac{2.209}{4} [/tex]

[tex]\qquad \sf  \therefore \: t = - 9.052 \: \: \: or \: \: \: t = 0.552[/tex]

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