Question

Neeed help more more please uwu

Answer 1

${ \qquad\qquad\huge\underline{{\sf Answer}}}$

Here we go ~

Let's calculate its discriminant ~

$\qquad \sf \dashrightarrow \: {t}^{2} + \cfrac{17}{2} t - 5 = 0$

[ Multiply both sides by 2 ]

$\qquad \sf \dashrightarrow \: 2 {t}^{2} + 17t - 10$

• a = 2

• b = 17

• c = 10

$\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac$

$\qquad \sf \dashrightarrow \: d = (17) {}^{2} - (4 \times 2 \times - 10)$

$\qquad \sf \dashrightarrow \: d = 289 - ( - 80)$

$\qquad \sf \dashrightarrow \: d = 369$

$\qquad \sf \dashrightarrow \: \sqrt {d }= 3 \sqrt{41} \approx19.209$

So, by quadratic formula :

$\qquad \sf \dashrightarrow \: t = \dfrac{ - {b}^{} \pm \sqrt{d} }{2a}$

$\qquad \sf \dashrightarrow \: t = \dfrac{ - {17}^{} \pm \sqrt{369} }{2 \times 2}$

$\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 17 - 19.209}{4} \: \: and \: \: t = \dfrac{-17+19.209}{4}$

$\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 36.209}{4} \: \: and \: \: t = \dfrac{2.209}{4}$

$\qquad \sf \therefore \: t = - 9.052 \: \: \: or \: \: \: t = 0.552$