Question

Solve quadratic equation in x by factorization method.
a2 x2 + (a2 + b2) x + b² = 0;​

Answer 1

Step-by-step explanation:

Given:-

a^2 x^2 + (a^2 + b^2) x + b^2= 0

To find:-

Solve quadratic equation in x by factorization method for a^2 x^2 + (a^2 + b^2) x + b^2= 0

Solution:-

Given quadratic equation is

a^2 x^2 + (a^2 + b^2) x + b^2= 0

=>a^2 x^2 + a^2 x + b^2 x + b^2= 0

=>a^2 x (x + 1) + b^2 (x + 1) = 0

=>(x + 1) (a^2 x + b^2) = 0

=>x + 1 = 0 (or) a^2 x + b^2 = 0

=>x = -1 (or) a^2 x = -b^2

=>x = -1 (or) x = -b^2/a^2

Therefore, x = -1 and -b^2/a^2

Answer:-

The values of x are -1 and -b^2/a^2

The roots of the given quadratic equation are

-1 and -b^2/a^2

Used Method:-

• Factorization method

Additional information:-

• An equation of the degree is two is called a quadratic equation.
• The standard form of a quadratic equation is ax^2+bx+c=0.
• A quadratic equation has at most two roots.
• We use factorization method,quadratic formula method (Sridharacharya method) for solving a quadratic equation.