Question

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Solve the equation with the quadratic formula *
10) 3x² =-10x – 5
1-5+2V10 -5 - 2V10
A)
3
3
-5+ V10 -5 - V10
B)
3
3
25
C) -4
4
15+ V10 5 - V10
D)
33

Answer 1

`\huge \red {\bigg \{( - 5 + √(10))/(3), \: \: ( - 5 - √(10))/(3)\bigg \}}`

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 * 3} \\ x = \frac{ - 10 \pm \sqrt{ {100} - 60}}{6} \\ x = ( - 10 \pm √(40))/(6) \\ x = ( - 10 \pm2 √(10))/(6) \\ x = ( 2(- 5 \pm √(10)))/(6) \\ x = ( - 5 \pm √(10))/(3) \\ x = \purple{ \bold{\bigg \{( - 5 + √(10))/(3), \: \: ( - 5 - √(10))/(3)\bigg \}}}`

Answer 2

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

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