Question

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Answer 1

Answer:

$\huge \red {\bigg \{\frac{ - 5 + \sqrt{10}}{3}, \: \: \frac{ - 5 - \sqrt{10}}{3}\bigg \}}$

Step-by-step explanation:

$3 {x}^{2} = - 10x - 5 \\ 3 {x}^{2} + 10x + 5 = 0 \\ equating \: it \: with \\ a {x}^{2} + bx + c = 0 \\ a = 3 \: \: b = 10 \: \: c = 5 \\ now \: by \: quadratic \: formula \\ x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\ plug \: a = 3 \: \: b = 10 \: \: c = 5 \: in \: the \\ above \: formula \\ x = \frac{ - 10 \pm \sqrt{ {(10)}^{2} - 4(3)(5) }}{2 \times 3} \\ x = \frac{ - 10 \pm \sqrt{ {100} - 60}}{6} \\ x = \frac{ - 10 \pm \sqrt{40}}{6} \\ x = \frac{ - 10 \pm2 \sqrt{10}}{6} \\ x = \frac{ 2(- 5 \pm \sqrt{10})}{6} \\ x = \frac{ - 5 \pm \sqrt{10}}{3} \\ x = \purple{ \bold{\bigg \{\frac{ - 5 + \sqrt{10}}{3}, \: \: \frac{ - 5 - \sqrt{10}}{3}\bigg \}}}$

Answer 2

Answer:

B) x = (-5 + √10)/3 and (-5 - √10)/3 is the answer.

Step-by-step explanation:

3x² + 10x + 5 = 0

a = 3

b = 10

c = 5

Finding the Discriminant (D),

D = b² - 4ac

D = 10² - 4 × 3 × 5

D = 100 - 60

D = 40

√D = 2√10

Using quadratic formula,

x = (-b ± √D)/2a

x = (-b + √D)/2a

x = (-10 + 2√10)/2 × 3

Taking out the common factor 2,

x = (-5 + √10)/3

Similarly,

x = (-b - √D)/2a

x = (-10 - 2√10)/2 × 3

x = (-5 - √10)/3