1.

Solve the following quadratic equations by factorization:\(x^2+(a+\frac{1}{a})x+1 = 0\)

Answer»

In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

\(x^2+(a+\frac{1}{a})x+1=0\)

⇒ ax2 +a2x + x + a =0 

⇒ ax(x + a) + 1(x + a) = 0 

⇒ (ax + 1)(x + a) = 0 

⇒ x = -a, -1/a



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