Question

2x^2–4x–2=0, solve the following quadratic equation ​

Answer 1

Answer:

2x^2-2x-2x-2=0

2x(x-1)-2(x-1)=0

(x-1)(2x-2)=0

x-1=0 or 2x-2=0

x=1 or x= 1

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Answer 2

Answer:

2.414 and -0.414

Step-by-step explanation:

$2x^{2} -4x-2=0$

Formulae for finding the quadratic equation

$x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}$  [∵  $+- =plus (or) minus$]

Determine the quadratic equation's coefficients a,b,c

a = 2

b = -4

c = -2

Substitute the values of a,b,c in the formulae

$x=\frac{-(-4)+-\sqrt{(-4)^{2}-4(2)(-2) } }{2(2)}$

$x=\frac{4+-\sqrt{16-(-16) } }{4}$

$x=\frac{4+-\sqrt{(16+16) } }{4}$

$x=\frac{4+-\sqrt{32} }{4}$  

$x=\frac{4+-4\sqrt{2} }{4}$   [∵$\sqrt{32} =4\sqrt{2}$]

Now separate the equations

$x_{1} =\frac{4+4\sqrt{2} }{4}$

$x_{2} =\frac{4-4\sqrt{2} }{4}$

By simplifying we get

$x_{1} = 2.414\\x_{2} =-0.414$

∴The Quadratic Equations are 2.414 and -0.414

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