Question

what are the roots of the quadratic equation x2 =9​

Answer 1

$\sf{Solution}$

Step-by-step-explanation:-

Given :-

x² = 9

To find :-

Roots of Quadratic equation

Concept:-

Hence It is a Quadratic equation If has 2 roots

It should be in form of general of Quadratic equation

The general form of Quadratic equation = ax² +bx+c=0

So, convert into general form and we can find roots

Formula implemented:-

a²-b² = (a+b)(a-b)

___________________________

Solution:-

x² = 9

Transpose 9 to RHS

x² - 9 = 0

9 can be written as 3²

x² - 3² = 0

It is in form of a²-b²

We know formula Algebraic identity

a²- b² = (a + b)(a-b)

So,

x² - 3² = 0

(x + 3)(x-3) = 0

Equate each of factor to 0

x + 3 =0

x = -3

x -3 =0

x =3

So, the roots of x²-9 = +3 , -3

________________________

Know more about Quadratic equation

Quadratic equation has two roots

The nature of roots can be determined by Discriminant

Discriminant is denoted by d

Discriminant of Quadratic equation is b²-4ac

Nature of roots

If D>0 roots are real & distinct

D <0 Roots are complex & conjugate

D = 0 roots are real & equal

Answer 2

Answer:

$\sf{Solution}$

Step-by-step-explanation:-

Given :-

x² = 9

To find :-

Roots of Quadratic equation

Concept:-

Hence It is a Quadratic equation If has 2 roots

It should be in form of general of Quadratic equation

The general form of Quadratic equation = ax² +bx+c=0

So, convert into general form and we can find roots

Formula implemented:-

a²-b² = (a+b)(a-b)

___________________________

Solution:-

x² = 9

Transpose 9 to RHS

x² - 9 = 0

9 can be written as 3²

x² - 3² = 0

It is in form of a²-b²

We know formula Algebraic identity

a²- b² = (a + b)(a-b)

So,

x² - 3² = 0

(x + 3)(x-3) = 0

Equate each of factor to 0

x + 3 =0

x = -3

x -3 =0

x =3

So, the roots of x²-9 = +3 , -3

________________________

Know more about Quadratic equation

Quadratic equation has two roots

The nature of roots can be determined by Discriminant

Discriminant is denoted by d

Discriminant of Quadratic equation is b²-4ac

Nature of roots

If D>0 roots are real & distinct

D <0 Roots are complex & conjugate

D = 0 roots are real & equal