Question

Solve the quadratic equation:- X^2-x-0=3

Answer 1

x² - x - 0 = 3

x² - x - 3 = 0



On comparing the obtained equation with ( ax² + bx + c = 0 ), we get

a = 1
b = - 1
c = - 3





So, discriminant = b^2 - 4ac
=> ( - 1 )^2 - 4( 1 × -3 )
=> 1 + 12
=> 13




Then, Applying quadratic formula,


$x = \frac{ - b + \sqrt{discriminant} }{2a} \: \: \: \: \: \: or \: \: \: \: x = \frac{ - b - \sqrt{discriminant} }{2a} \\ \\ \\ x = \frac{ - ( - 1) + \sqrt{13} }{ \: 2(1)} \: \: \: \: \: or \: \: \: \: \: x = \frac{ - 1 - \sqrt{13} }{2(1)} \\ \\ \\ x = \frac{1 + \sqrt{13} }{2} \: \: \: \: or \: \: \: \: x = \frac{1 - \sqrt{13} }{2}$

Answer 2

solution

x²-x-0=3

using formula

x=-b₊or₋√b²-4ac/2a

where a=1, b=1-, c=-3

=-1₊or₋√1²-4(-3)/2(1)

=₋1₊or₋√1+12/2

=-1+or-√13/2

⇒x=(-1+√13)/2 or x=(-1-√13)/2