Question

factorization : x^2+x-1​

Answer 1

We can also factorize a quadratic polynomial, using quadratic formula…

Method:

(1) : First get the value of x for the above polynomial p(x) = 0

(2) : Then take additive inverse of those values of x.

(3) : Then each value is added to x separately to get its factors.

P(x) = x² + x - 1 = 0

=> x = {-1+ - √(1² + 4)}/2 ( using quadratic formula)

=> x = (-1 +√5)/2 & (-1 -√5)/2

Additive inverse of 1st value = -(-1+√5)/2

=(1-√5)/2

Additive inverse of 2nd value = -(-1-√5)/2

= (1+√5)/2

Hence, factors are..

= x + {(1-√5)/2} & x +{(1+√5)/2}

= (2x +1-√5) /2 & (2x +1 +√5)/2

= (1/4) ( 2x+1-√5) (2x+1+√5)

So, factors are (1/4) (2x+1-√5) (2x+1+√5)