Question

factorial x2-2root5x+3

Answer 1

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Answer 2

Answer:

The factors are $x=\sqrt{5}+\sqrt{2},\sqrt{5}-\sqrt{2}$

Step-by-step explanation:

Given : Quadratic equation - $x^2-2\sqrt{5}x+3$

To find : Factorizing the given quadratic equation.

Solution :

Solving by discriminant method  

General form - $ax^2+bx+c=0$

$D=b^2-4ac$

Solution is $x=\frac{-b\pm\sqrt{D}}{2a}$

Given equation is $x^2-2\sqrt{5}x+3=0$

where a=1 ,$b=-2\sqrt{5}$ , c=3

$D=b^2-4ac$

$D=(-2\sqrt{5})^2-4(1)(3)$

$D=20-12$

$D=8$

Solution is $x=\frac{-b\pm\sqrt{D}}{2a}$

$x=\frac{-(-2\sqrt{5})\pm\sqrt{8}}{2(1)}$

$x=\frac{2\sqrt{5}\pm2\sqrt{2}}{2}$

$x=\sqrt{5}\pm\sqrt{2}$

Therefore, The factors are $x=\sqrt{5}+\sqrt{2},\sqrt{5}-\sqrt{2}$