Question

X²+10x+2=0 quadratic equation using formula

Answer 1

Answer:

( - 5 ± √ 23 )

Step-by-step explanation:

Given :

x² + 10 x + 2 = 0

We know :

x = ( - b ± ( √ ( b² - 4 a c ) ) / 2 a

Putting values here we get :

= > x = ( - 10 ± √ ( 10² - 4 × 1 × 2 ) ) / 2

= > x = ( - 10 ± √ ( 100 - 8 ) ) / 2

= > x = ( - 10 ± √ 92 ) / 2

= > x = ( - 5 ± √ 23 )

Therefore , value of x is  ( - 5 ± √ 23 ) .

Answer 2

$\sf{f(x) = {x}^{2} + 10x + 2 = 0 } \\ \\ \sf{According \ to \ quadratic \ Equation \ Formula \ - } \\ \\ \sf{ Let \ the \ roots \ be \ \alpha \ and \ \beta . } \\ \\ \sf{ \alpha , \ \beta = \dfrac{ -b + D }{ 2a } , \ \dfrac{ -b - D }{ 2a } } \\ \\ \sf{ \bold{ Where \ - }} \\ \\ \sf{ D \ is \ the \ discriminant . } \\ \\ \sf{ D = \sqrt{ {b}^2 - 4ac} } \\ \\ \sf{ a \ is \ the \ coefficent \ of \ {x}^2 } \\ \\ \sf{ b \ is \ the \ coefficent \ of \ {x} } \\ \\ \sf{ c \ is \ the \ constant }$

$\sf{ Substituting \ the \ given \ values \ - } \\ \\ \sf{ D = \sqrt{ {(10)}^2 - 4 \times 2 \times 1 } } \\ \\ \sf{ D = \sqrt{92} \approx 9.6 } \\ \\ \sf{ \alpha = \dfrac{ -10 + 9.6 }{2} = \dfrac{ - 0.4 }{ 2 } = -0.2 } \\ \\ \sf{ \beta = \dfrac{ -10 - 9.6 }{ 2 } = \dfrac{ -19.6 }{ 2 } = - 9.8 }$