Question

${x}^{2} - 4x + 4 = 0$​

Answer 1

x

2

−4x+4=0

x

2

−2x−2x+4=0

x(x−2)−2(x−2)=0

(x−2)(x−2)=0

x=2,2 hope it's helpful if it is then please mark me as brainliest

Answer 2

$\large\underline{\sf{Solution-}}$

Given quadratic equation is

$\rm :\longmapsto\: {x}^{2} - 4x + 4 = 0$

can be rewritten as using splitting of middle terms,

$\rm :\longmapsto\: {x}^{2} - 2x - 2x + 4 = 0$

$\rm :\longmapsto\:x(x - 2) - 2(x - 2) = 0$

$\rm :\longmapsto\:(x - 2)(x - 2) = 0$

$\bf\implies \:x = 2 \: \: or \: \: 2$

Aliter Method [ Completing Squares method ]

Given Quadratic equation is

$\rm :\longmapsto\: {x}^{2} - 4x + 4 = 0$

can be rewritten as

$\rm :\longmapsto\: {x}^{2} - 4x + {2}^{2} = 0$

$\rm :\longmapsto\: {x}^{2} - 2 \times x \times 2 + {2}^{2} = 0$

We know, .

$\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{2} - 2xy + {y}^{2} = {(x + y)}^{2} \: \: }}$

$\rm :\longmapsto\: {(x - 2)}^{2} = 0$

$\bf\implies \:x = 2 \: \: or \: \: 2$

Aliter Method [ Quadratic Formula ]

Given quadratic equation is

$\rm :\longmapsto\: {x}^{2} - 4x + 4 = 0$

The solution of quadratic equation using Quadratic formula is

$\red{\rm :\longmapsto\:\boxed{\tt{ x = \frac{ - b \: \pm \: \sqrt{ {b}^{2} - 4ac} }{2a}}}}$

So, here,

$\rm :\longmapsto\:a = 1$

$\rm :\longmapsto\:b = - 4$

$\rm :\longmapsto\:c = 4$

So, on substituting the values, we get

$\rm :\longmapsto\:x = \dfrac{ - ( - 4) \: \pm \: \sqrt{ {(4)}^{2} - 4(1)(4) } }{2 \times 1}$

$\rm :\longmapsto\:x = \dfrac{ 4 \: \pm \: \sqrt{ 0} }{2}$

$\rm :\longmapsto\:x = \dfrac{ 4 }{2}$

$\bf\implies \:x = 2$

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Additional Information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac