Question

Which are the solutions of the quadratic equation? x2 = –5x – 3

Answer 1

Find out the solutions of the quadratic equation.

x² = –5x – 3

To prove

As the quadratic equation be.

x² + 5x + 3 = 0

Discriminant Formula

`x = \frac{-b\pm\sqrt{b^(2) -4ac} }{2a}`

As a = 1 , b = 5 , c = 3

Put in the formula

`x = \frac{-5\pm\sqrt{5^(2) -4* 1* 3} }{2* 1}`

`x = (-5\pm√(25 -12) )/(2* 1)`

`x = (-5\pm√(13) )/(2* 1)`

Thus the solutions of x² = –5x – 3 are

`x = (-5\ +√(13) )/(2)`

and

`x = (-5\ -√(13) )/(2)`

Answer 2

`x^2=-5x-3\\x^2+5x+3=0\\\\a=1;\ b=5;\ c=3\\\Delta=b^2-4ac\\\\\Delta=5^2-4\cdot1\cdot3=25-12=13 \ \textgreater \ 0\\\\therefore\\x_1=(-b-\sqrt\Delta)/(2a)\ and\ x_2=(-b+\sqrt\Delta)/(2a)\\\\x_1=(-5-√(13))/(2\cdot1)=\boxed{(-5-√(13))/(2)}\\\\x_2=(-5+√(13))/(2\cdot1)=\boxed{(-5+√(13))/(2)}`